diff --git a/docs/source/gradient_solver.rst b/docs/source/gradient_solver.rst
index 81c5a56..4e3fc71 100644
--- a/docs/source/gradient_solver.rst
+++ b/docs/source/gradient_solver.rst
@@ -1,7 +1,7 @@
-.. default-domain:: cpp
-
 .. highlight:: c++
 
+.. default-domain:: cpp
+
 .. cpp:namespace:: ceres
 
 .. _chapter-gradient_problem_solver:
@@ -103,7 +103,7 @@
    behavior of the solver. We list the various settings and their
    default values below.
 
-.. function:: bool GradientProblemSolver::Options::IsValid(string* error) const
+.. function:: bool GradientProblemSolver::Options::IsValid(std::string* error) const
 
    Validate the values in the options struct and returns true on
    success. If there is a problem, the method returns false with
@@ -388,14 +388,14 @@
    #. ``it`` is the time take by the current iteration.
    #. ``tt`` is the total time taken by the minimizer.
 
-.. member:: vector<IterationCallback> GradientProblemSolver::Options::callbacks
+.. member:: std::vector<IterationCallback> GradientProblemSolver::Options::callbacks
 
    Callbacks that are executed at the end of each iteration of the
    :class:`Minimizer`. They are executed in the order that they are
    specified in this vector. By default, parameter blocks are updated
    only at the end of the optimization, i.e., when the
    :class:`Minimizer` terminates. This behavior is controlled by
-   :member:`GradientProblemSolver::Options::update_state_every_variable`. If
+   :member:`GradientProblemSolver::Options::update_state_every_iteration`. If
    the user wishes to have access to the update parameter blocks when
    his/her callbacks are executed, then set
    :member:`GradientProblemSolver::Options::update_state_every_iteration`
@@ -420,12 +420,12 @@
 
    Summary of the various stages of the solver after termination.
 
-.. function:: string GradientProblemSolver::Summary::BriefReport() const
+.. function:: std::string GradientProblemSolver::Summary::BriefReport() const
 
    A brief one line description of the state of the solver after
    termination.
 
-.. function:: string GradientProblemSolver::Summary::FullReport() const
+.. function:: std::string GradientProblemSolver::Summary::FullReport() const
 
    A full multiline description of the state of the solver after
    termination.
@@ -444,7 +444,7 @@
 
    The cause of the minimizer terminating.
 
-.. member:: string GradientProblemSolver::Summary::message
+.. member:: std::string GradientProblemSolver::Summary::message
 
    Reason why the solver terminated.
 
@@ -458,7 +458,7 @@
    Cost of the problem (value of the objective function) after the
    optimization.
 
-.. member:: vector<IterationSummary> GradientProblemSolver::Summary::iterations
+.. member:: std::vector<IterationSummary> GradientProblemSolver::Summary::iterations
 
    :class:`IterationSummary` for each minimizer iteration in order.
 
diff --git a/docs/source/gradient_tutorial.rst b/docs/source/gradient_tutorial.rst
index fb26cb7..261a5e9 100644
--- a/docs/source/gradient_tutorial.rst
+++ b/docs/source/gradient_tutorial.rst
@@ -2,6 +2,8 @@
 
 .. default-domain:: cpp
 
+.. cpp:namespace:: ceres
+
 .. _chapter-gradient_tutorial:
 
 ==================================
diff --git a/docs/source/modeling_faqs.rst b/docs/source/modeling_faqs.rst
index a2704d8..2e4f6f2 100644
--- a/docs/source/modeling_faqs.rst
+++ b/docs/source/modeling_faqs.rst
@@ -37,7 +37,7 @@
    automatic and numeric differentiation. See
    :class:`CostFunctionToFunctor`.
 
-#. When using Quaternions,  consider using :class:`QuaternionParameterization`.
+#. When using Quaternions,  consider using :class:`QuaternionManifold`.
 
    `Quaternions <https://en.wikipedia.org/wiki/Quaternion>`_ are a
    four dimensional parameterization of the space of three dimensional
@@ -47,14 +47,14 @@
    associate a local parameterization with parameter blocks
    representing a Quaternion. Assuming that the order of entries in
    your parameter block is :math:`w,x,y,z`, you can use
-   :class:`QuaternionParameterization`.
+   :class:`QuaternionManifold`.
 
    .. NOTE::
 
      If you are using `Eigen's Quaternion
      <http://eigen.tuxfamily.org/dox/classEigen_1_1Quaternion.html>`_
      object, whose layout is :math:`x,y,z,w`, then you should use
-     :class:`EigenQuaternionParameterization`.
+     :class:`EigenQuaternionManifold`.
 
 
 #. How do I solve problems with general linear & non-linear
@@ -81,8 +81,9 @@
    and lower bounds constraints on the parameter blocks.
 
    The trick described above for dealing with inequality
-   constraints will **not** work for equality constraints.
+   constraints will **not** work.. default-domain:: cpp                                                                                                                  |
+                                        for equality constraints.
 
 #. How do I set one or more components of a parameter block constant?
 
-   Using :class:`SubsetParameterization`.
+   Using :class:`SubsetManifold`.
diff --git a/docs/source/nnls_covariance.rst b/docs/source/nnls_covariance.rst
index 2c3c05d..ece6f58 100644
--- a/docs/source/nnls_covariance.rst
+++ b/docs/source/nnls_covariance.rst
@@ -1,3 +1,4 @@
+.. highlight:: c++
 
 .. default-domain:: cpp
 
@@ -49,7 +50,7 @@
 covariance of :math:`y`, then the maximum likelihood problem to be
 solved is
 
-.. math:: x^* = \arg \min_x f'(x) S^{-1} f(x)
+o.. math:: x^* = \arg \min_x f'(x) S^{-1} f(x)
 
 and the corresponding covariance estimate of :math:`x^*` is given by
 
@@ -302,7 +303,7 @@
    entire documentation for :class:`Covariance::Options` before using
    :class:`Covariance`.
 
-.. function:: bool Covariance::Compute(const vector<pair<const double*, const double*> >& covariance_blocks, Problem* problem)
+.. function:: bool Covariance::Compute(const std::vector<std::pair<const double*, const double*> >& covariance_blocks, Problem* problem)
 
    Compute a part of the covariance matrix.
 
@@ -378,7 +379,7 @@
  Covariance::Options options;
  Covariance covariance(options);
 
- vector<pair<const double*, const double*> > covariance_blocks;
+ std::vector<std::pair<const double*, const double*> > covariance_blocks;
  covariance_blocks.push_back(make_pair(x, x));
  covariance_blocks.push_back(make_pair(y, y));
  covariance_blocks.push_back(make_pair(x, y));
diff --git a/docs/source/nnls_modeling.rst b/docs/source/nnls_modeling.rst
index e393148..512834c 100644
--- a/docs/source/nnls_modeling.rst
+++ b/docs/source/nnls_modeling.rst
@@ -1,7 +1,7 @@
-.. default-domain:: cpp
-
 .. highlight:: c++
 
+.. default-domain:: cpp
+
 .. cpp:namespace:: ceres
 
 .. _`chapter-nnls_modeling`:
@@ -83,11 +83,11 @@
       virtual bool Evaluate(double const* const* parameters,
                             double* residuals,
                             double** jacobians) const = 0;
-      const vector<int32>& parameter_block_sizes();
+      const std::vector<int32>& parameter_block_sizes();
       int num_residuals() const;
 
      protected:
-      vector<int32>* mutable_parameter_block_sizes();
+      std::vector<int32>* mutable_parameter_block_sizes();
       void set_num_residuals(int num_residuals);
     };
 
@@ -842,7 +842,7 @@
        //  my_cost_function produces N residuals
        CostFunction* my_cost_function = ...
        CHECK_EQ(N, my_cost_function->num_residuals());
-       vector<CostFunction*> conditioners;
+       std::vector<CostFunction*> conditioners;
 
        //  Make N 1x1 cost functions (1 parameter, 1 residual)
        CostFunction* f_1 = ...
@@ -1190,7 +1190,7 @@
 `corrector.cc <https://github.com/ceres-solver/ceres-solver/blob/master/internal/ceres/corrector.cc#L51>`_
 
 
-:class:`Manifolds`
+:class:`Manifold`
 ==================
 
 .. class:: Manifold
@@ -2014,7 +2014,7 @@
        on a :class:`Problem` with a non-null evaluation callback is an
        error.
 
-.. function:: ResidualBlockId Problem::AddResidualBlock(CostFunction* cost_function, LossFunction* loss_function, const vector<double*> parameter_blocks)
+.. function:: ResidualBlockId Problem::AddResidualBlock(CostFunction* cost_function, LossFunction* loss_function, const std::vector<double*> parameter_blocks)
 
 .. function:: template <typename Ts...> ResidualBlockId Problem::AddResidualBlock(CostFunction* cost_function, LossFunction* loss_function, double* x0, Ts... xs)
 
@@ -2055,9 +2055,9 @@
       double x1[] = {1.0, 2.0, 3.0};
       double x2[] = {1.0, 2.0, 5.0, 6.0};
       double x3[] = {3.0, 6.0, 2.0, 5.0, 1.0};
-      vector<double*> v1;
+      std::vector<double*> v1;
       v1.push_back(x1);
-      vector<double*> v2;
+      std::vector<double*> v2;
       v2.push_back(x2);
       v2.push_back(x1);
 
@@ -2234,24 +2234,24 @@
 
    Is the given parameter block present in the problem or not?
 
-.. function:: void Problem::GetParameterBlocks(vector<double*>* parameter_blocks) const
+.. function:: void Problem::GetParameterBlocks(std::vector<double*>* parameter_blocks) const
 
    Fills the passed ``parameter_blocks`` vector with pointers to the
    parameter blocks currently in the problem. After this call,
    ``parameter_block.size() == NumParameterBlocks``.
 
-.. function:: void Problem::GetResidualBlocks(vector<ResidualBlockId>* residual_blocks) const
+.. function:: void Problem::GetResidualBlocks(std::vector<ResidualBlockId>* residual_blocks) const
 
    Fills the passed `residual_blocks` vector with pointers to the
    residual blocks currently in the problem. After this call,
    `residual_blocks.size() == NumResidualBlocks`.
 
-.. function:: void Problem::GetParameterBlocksForResidualBlock(const ResidualBlockId residual_block, vector<double*>* parameter_blocks) const
+.. function:: void Problem::GetParameterBlocksForResidualBlock(const ResidualBlockId residual_block, std::vector<double*>* parameter_blocks) const
 
    Get all the parameter blocks that depend on the given residual
    block.
 
-.. function:: void Problem::GetResidualBlocksForParameterBlock(const double* values, vector<ResidualBlockId>* residual_blocks) const
+.. function:: void Problem::GetResidualBlocksForParameterBlock(const double* values, std::vector<ResidualBlockId>* residual_blocks) const
 
    Get all the residual blocks that depend on the given parameter
    block.
@@ -2327,7 +2327,7 @@
     :func:`Problem::EvaluateResidualBlock`).
 
 
-.. function:: bool Problem::Evaluate(const Problem::EvaluateOptions& options, double* cost, vector<double>* residuals, vector<double>* gradient, CRSMatrix* jacobian)
+.. function:: bool Problem::Evaluate(const Problem::EvaluateOptions& options, double* cost, std::vector<double>* residuals, std::vector<double>* gradient, CRSMatrix* jacobian)
 
    Evaluate a :class:`Problem`. Any of the output pointers can be
    ``nullptr``. Which residual blocks and parameter blocks are used is
@@ -2383,7 +2383,7 @@
 
    Options struct that is used to control :func:`Problem::Evaluate`.
 
-.. member:: vector<double*> Problem::EvaluateOptions::parameter_blocks
+.. member:: std::vector<double*> Problem::EvaluateOptions::parameter_blocks
 
    The set of parameter blocks for which evaluation should be
    performed. This vector determines the order in which parameter
@@ -2399,7 +2399,7 @@
    should NOT point to new memory locations. Bad things will happen if
    you do.
 
-.. member:: vector<ResidualBlockId> Problem::EvaluateOptions::residual_blocks
+.. member:: std::vector<ResidualBlockId> Problem::EvaluateOptions::residual_blocks
 
    The set of residual blocks for which evaluation should be
    performed. This vector determines the order in which the residuals
diff --git a/docs/source/nnls_solving.rst b/docs/source/nnls_solving.rst
index 4b8b171..226e5f6 100644
--- a/docs/source/nnls_solving.rst
+++ b/docs/source/nnls_solving.rst
@@ -1,7 +1,7 @@
-.. default-domain:: cpp
-
 .. highlight:: c++
 
+.. default-domain:: cpp
+
 .. cpp:namespace:: ceres
 
 .. _chapter-nnls_solving:
@@ -2091,6 +2091,13 @@
    :member:`Solver::Options::update_state_every_iteration` to
    ``true``.
 
+   See `examples/iteration_callback_example.cc
+   <https://ceres-solver.googlesource.com/ceres-solver/+/master/examples/iteration_callback_example.cc>`_
+   for an example of an :class:`IterationCallback` that uses
+   :member:`Solver::Options::update_state_every_iteration` to log
+   changes to the parameter blocks over the course of the
+   optimization.
+
    The solver does NOT take ownership of these pointers.
 
 :class:`ParameterBlockOrdering`
@@ -2307,6 +2314,10 @@
   #. ``SOLVER_CONTINUE`` indicates that the solver should continue
      optimizing.
 
+  The return values can be used to implement custom termination
+  criterion that supercede the iteration/time/tolerance based
+  termination implemented by Ceres.
+
   For example, the following :class:`IterationCallback` is used
   internally by Ceres to log the progress of the optimization.
 
@@ -2346,6 +2357,12 @@
     };
 
 
+  See `examples/evaluation_callback_example.cc
+  <https://ceres-solver.googlesource.com/ceres-solver/+/master/examples/iteration_callback_example.cc>`_
+  for another example that uses
+  :member:`Solver::Options::update_state_every_iteration` to log
+  changes to the parameter blocks over the course of the optimization.
+
 
 :class:`CRSMatrix`
 ==================
diff --git a/docs/source/nnls_tutorial.rst b/docs/source/nnls_tutorial.rst
index ba68a78..3268e71 100644
--- a/docs/source/nnls_tutorial.rst
+++ b/docs/source/nnls_tutorial.rst
@@ -2,6 +2,8 @@
 
 .. default-domain:: cpp
 
+.. cpp:namespace:: ceres
+
 .. _chapter-nnls_tutorial:
 
 ========================