diff --git a/exercises/exercise-mainfile/README.md b/exercises/exercise-mainfile/README.md
index 5e084a912b3f5bec6c80c47124f622d5f8a5f421..0f8ee4742f6c7cf62a4340b88714efd317d5dd87 100644
--- a/exercises/exercise-mainfile/README.md
+++ b/exercises/exercise-mainfile/README.md
@@ -3,11 +3,11 @@
 
 ## Problem set-up
 
-This exercise will make you familiar the program sequence in DuMuX and how different levels of complexity can be realized in the main file according to the complexity of your physical problem.
+This exercise will make you familiar with the program sequence in DuMu<sup>X</sup> and how different levels of complexity can be realized in the main file according to the complexity of your physical problem.
 
 In order to do so, there are three examples of one phase flow problems. Two examples (a and b) are stationary problems and the third example (c) is an instationary problem.
 
-The stationary examples differ in the `fluidssystems` they are using, which means they differ in the fluid properties (e.g. density, thermal conductivity etc). The first problem (a) uses an incompressible fluid, i.e. the density does not change when pressure changes. This makes it possible to solve the system linearly. The second problem uses a compressible fluid, that means the density is a function of pressure and we need to use a nonlinear solver.
+The stationary examples differ in the `FluidSystem` they are using, which means they differ in the fluid properties (e.g. density, thermal conductivity etc). The first problem (a) uses an incompressible fluid, i.e. the density does not change when pressure changes. This makes it possible to solve the system linearly. The second problem uses a compressible fluid, that means the density is a function of pressure and we need to use a nonlinear solver.
 
 To summarize, the problems differ in:
 * exercise mainfile a: a one-phase incompressible, stationary problem
@@ -184,7 +184,7 @@ paraview 1p_incompressible_stationary.pvd
 <hr>
 
 In the input file `exercise_mainfile_a.input`, you will see that there is a variable `BaseEpsilon`.
-This defines the base for the epsilon used in the numeric differentiation.
+This defines the base value for the epsilon used in the numeric differentiation.
 If that value is too small, you will see that the solution of the numeric differentiation is not correct.
 Change that value to $1 \cdot 10^{-15}$ and have a look at the solution.
 
diff --git a/exercises/exercise-mainfile/properties.hh b/exercises/exercise-mainfile/properties.hh
index 15544aeff65ef7c4da33b3095506544d1f845f24..ce835d308f37dad995e6ca7956896d47c037f399 100644
--- a/exercises/exercise-mainfile/properties.hh
+++ b/exercises/exercise-mainfile/properties.hh
@@ -38,7 +38,7 @@
 
 #include <dumux/porousmediumflow/1p/model.hh>
 // TODO: dumux-course-task 3
-// uncomment the incompressiblelocalresidual which is a specialization of the standard immisible localresidual for one phase incompressible cases and provides an analytic jacobian.
+// uncomment the incompressiblelocalresidual which is a specialization of the standard immiscible localresidual for one phase incompressible cases and provides an analytic jacobian.
 // #include <dumux/porousmediumflow/1p/incompressiblelocalresidual.hh>
 
 #include "1pspatialparams.hh"