diff --git a/docs/source/tutorials/kim_SW_Si.ipynb b/docs/source/tutorials/kim_SW_Si.ipynb
index 0252d579..3a1b1d86 100644
--- a/docs/source/tutorials/kim_SW_Si.ipynb
+++ b/docs/source/tutorials/kim_SW_Si.ipynb
@@ -44,7 +44,7 @@
     "   use KLIFF to train potentials. It should not be used to train any potential for real\n",
     "   simulations.</p></div>\n",
     "\n",
-    "Let's first import the modules that will be used in this example.\n",
+    "Let's first import the modules that will be used in this example.  In python, we write:\n",
     "\n"
    ]
   },
@@ -75,7 +75,7 @@
     "## Model\n",
     "\n",
     "We first create a KIM model for the SW potential, and print out all the available\n",
-    "parameters that can be optimized (we call this ``model parameters``).\n",
+    "parameters that can be optimized (we call these the ``model parameters``).  Continuing in our python script we write\n",
     "\n"
    ]
   },
@@ -230,7 +230,7 @@
    "source": [
     "Here, we tell KLIFF to fit four parameters ``B``, ``gamma``, ``sigma``, and ``A`` of the\n",
     "SW model. The information for each fitting parameter should be provided as a list of\n",
-    "list, where the size of the outer list should be equal to the ``size`` of the parameter\n",
+    "lists, where the size of the outer list should be equal to the ``size`` of the parameter\n",
     "given by ``model.echo_model_params()``. For each inner list, you can provide either one,\n",
     "two, or three items.\n",
     "\n",
@@ -304,9 +304,9 @@
     "## Calculator\n",
     "\n",
     ":class:`~kliff.calculator.Calculator` is the central agent that exchanges information\n",
-    "and orchestrate the operation of the fitting process. It calls the model to compute the\n",
+    "and orchestrates the operation of the fitting process. It calls the model to compute the\n",
     "energy and forces and provide this information to the `Loss function`_ (discussed below)\n",
-    "to compute the loss. It also grabs the parameters from the optimizer and update the\n",
+    "to compute the loss. It also grabs the parameters from the optimizer and updates the\n",
     "parameters stored in the model so that the up-to-date parameters are used the next time\n",
     "the model is evaluated to compute the energy and forces. The calculator can be created\n",
     "by:\n",
@@ -542,7 +542,7 @@
    "metadata": {},
    "source": [
     "The minimization stops after running for 27 steps.  After the minimization, we'd better\n",
-    "save the model, which can be loaded later for the purpose to do a retraining or\n",
+    "save the model, which can be loaded later for the purpose of retraining or for function\n",
     "evaluations. If satisfied with the fitted model, you can also write it as a KIM model\n",
     "that can be used with LAMMPS_, GULP_, ASE_, etc. via the kim-api_.\n",
     "\n"
@@ -609,7 +609,7 @@
     "``kliff_model.pkl`` on the disk, and the third line writes out a KIM potential named\n",
     "``SW_StillingerWeber_1985_Si__MO_405512056662_006_kliff_trained``.\n",
     "\n",
-    ".. seealso::\n",
+    "- SeeAlso: \n",
     "   For information about how to load a saved model, see `doc.modules`.\n",
     "\n",
     "\n",