diff --git a/slides/materialsystem.md b/slides/materialsystem.md
index 22021f03eb3b82cb26e973caca96983322cf65f3..ac0c8bd944b246194b6f2d33ce9e9797bcb9427f 100644
--- a/slides/materialsystem.md
+++ b/slides/materialsystem.md
@@ -1,27 +1,38 @@
 ---
-title: The DuMuX Material System
+title: The DuMu^x^ Material System
 ---
 
+# Challenge
 
-## Challenges in simulating porous media
+## Flow in porous media
 
 * Highly heterogeneous distribution of parameters and complex nonlinear material laws
-
 * Strong interconnection of properties $\rightarrow$ difficult to achieve __modularity__
 
+$\rightarrow$ this also applies to other complex nonlinear equation systems.
+
+# How to achieve modularity?
+
 ## How to achieve modularity?
 
-- User-defined parameters and relationships:
+* User-defined parameters and functional relationships:
     - Components / Fluid system / Binary coefficients
     - Solid system
     - Fluid-matrix interactions
     - Chemistry
-- Dumux-specific containers and solvers:
-    - Fluid states
-    - Solid states
-    - Constraint solvers
+* State representations and solvers:
+    - Fluid states (data)
+    - Solid states (data)
+    - Constraint solvers / "flash" (algorithm)
+
+## How to achieve modularity?
 
+There is a library of `Components`,
+`FluidSystems`, `BinaryCoefficients`
+available in DuMu^x^. Can be used as is or can
+be a good start for a user implementation.
 
+More resources can be found [in the code documentation](https://dumux.org/docs/doxygen/master/group___material.html).
 
 # Components
 
@@ -29,14 +40,41 @@ title: The DuMuX Material System
 
 * Define **Thermodynamic relations** (e.g. molar mass, vapor pressure, density) of a **single chemical species** or a fixed mixture of species
 * Provide a convenient way to access these quantities
-* Not supposed to be used by models directly
 
 ## Example implementations
 
-* _H2O_ : pure water, properties by IAPWS-97 or simplified
-
+* _H2O_ : pure water properties by IAPWS-97
+* _SimpleH2O_ : A simple water implementation at standard conditions
 * _Brine_ : water with a given salt concentration
+* Many more, see [DuMu^x^ components docs](https://dumux.org/docs/doxygen/master/namespace_dumux_1_1_components.html)
+
+## Example interfaces
+
+```cpp
+static Scalar gasDensity(Scalar temperature, Scalar pressure)
+{
+    // Assume an ideal gas
+    return IdealGas::density(molarMass(), temperature, pressure);
+}
+```
 
+## Example interfaces
+
+```cpp
+static Scalar gasHeatCapacity(Scalar temperature, Scalar pressure)
+{
+    constexpr Scalar cpVapA = 19.25;
+    constexpr Scalar cpVapB = 0.05213;
+    constexpr Scalar cpVapC = 1.197e-5;
+    constexpr Scalar cpVapD = -1.132e-8;
+
+    return 1/molarMass()*(
+        cpVapA + temperature*(
+            cpVapB/2 + temperature*(cpVapC/3 + temperature*(cpVapD/4))
+        )
+    );
+}
+```
 
 # Fluid systems
 
@@ -50,9 +88,27 @@ Express the **thermodynamic relations between fluid quantities** (e.g. calculati
 ## Example implementations
 
 * _TwoPImmiscible_ : two immiscible fluid phases
-
 * _H2OAir_ : gas and liquid phase with components water and air
+* Many more, see [DuMu^x^ fluid systems docs](https://dumux.org/docs/doxygen/master/namespace_dumux_1_1_fluid_systems.html)
 
+## Example interface
+
+```cpp
+template <class FluidState>
+static Scalar heatCapacity(const FluidState& fluidState, int phaseIdx)
+{
+    const Scalar temperature = fluidState.temperature(phaseIdx);
+    const Scalar pressure = fluidState.pressure(phaseIdx);
+    if (phaseIdx == liquidPhaseIdx)
+        return H2O::liquidHeatCapacity(temperature, pressure); // neglect air
+    else if (phaseIdx == gasPhaseIdx)
+        return Air::gasHeatCapacity(temperature, pressure)
+                   * fluidState.moleFraction(gasPhaseIdx, AirIdx)
+               + H2O::gasHeatCapacity(temperature, pressure)
+                   * fluidState.moleFraction(gasPhaseIdx, H2OIdx);
+    ...
+}
+```
 
 # Binary coefficients
 
@@ -66,6 +122,23 @@ Express the **thermodynamic relations between fluid quantities** (e.g. calculati
 ## Example implementations
 
 * _H2O_Air_ : Henry coefficient, gas diffusion coefficient, liquid diffusion coefficent for water and air
+* More, see [DuMu^x^ binary coefficients docs](https://dumux.org/docs/doxygen/master/namespace_dumux_1_1_binary_coeff.html)
+
+## Example interface
+
+```cpp
+template <class Scalar>
+static Scalar gasDiffCoeff(Scalar temperature, Scalar pressure)
+{
+    // _H2O_Air_
+    constexpr Scalar theta = 1.8;
+    constexpr Scalar Daw = 2.13e-5;  /* reference value */
+    constexpr Scalar pg0 = 1.e5;     /* reference pressure */
+    constexpr Scalar T0 = 273.15;    /* reference temperature */
+    using std::pow;
+    return Daw*(pg0/pressure)*pow((temperature/T0), theta);
+}
+```
 
 
 # Solid systems
@@ -122,51 +195,33 @@ p_c = p_d S_e^{-1/\lambda}
 $\rightarrow$ the empirical parameters $p_d$ and $\lambda$ have to be specified
 
 
-# Chemistry
-
-## Chemistry
-
-Reactions between different components. They are extra models or are incoporated via the introduction of a source term.
-
-<img src="img/chemistry.png" width="350"/>
-
-
-## Example implementations
-
-Expresses the **electrochemical models for a fuel cell application**:
-
-* _Electrochemistry_ : for isothermal system
-* _Electrochemistryni_ : for non-isothermal system
-
-
 # Fluid states
 
 ## Fluid states
 
- * **Store** the complete thermodynamic configuration of a system at a given spatial and temporal position (e.g. saturation, mole fraction, enthalpy)
- * **Provide access** methods to all thermodynamic quantities (e.g. saturation, mole fraction, enthalpy)
+* **Store** the complete thermodynamic configuration of a system at a given spatial and temporal position (e.g. saturation, mole fraction, enthalpy)
+* **Provide access** methods to all thermodynamic quantities (e.g. saturation, mole fraction, enthalpy)
 
 <img src="img/fluidstate.png" width="800"/>
 
 
 ## Example implementations
 
- * _ImmiscibleFluidState_ : assumes immiscibility of the fluid phases. Phase compositions and fugacity coefficients do not need to be stored explicitly.
- * _CompositionalFluidState_ : assumes thermodynamic equilibrium, only a single temperature needs to be stored.
+* _ImmiscibleFluidState_ : assumes immiscibility of the fluid phases. Phase compositions and fugacity coefficients do not need to be stored explicitly.
+* _CompositionalFluidState_ : assumes thermodynamic equilibrium, only a single temperature needs to be stored.
 
 # Solid states
 
 ## Solid states
 
- * **Store** the complete solid configuration of a system at a given spatial and temporal position (e.g. solid volume fractions, solid heat capacity)
- * **Provide** access methods to all solid quantities (e.g. porosity, density, temperature)
+* **Store** the complete solid configuration of a system at a given spatial and temporal position (e.g. solid volume fractions, solid heat capacity)
+* **Provide** access methods to all solid quantities (e.g. porosity, density, temperature)
 
 <img src="img/solidstate.png" width="800"/>
 
 ## Example implementations
 
 * _InertSolidState_ : assumes an inert solid phase. Solid volume fractions do not change. This is the **default**.
-
 * _CompositionalSolidState_ : assumes a solid matrix composed out of two components. The volume fractions can change and properties such as heat capacity are adapted.
 
 # Constraint Solvers
@@ -191,8 +246,8 @@ _CompositionFromFugacities_ : takes all component fugacities, the temperature an
 
 ## Example: 2 phases, miscible
 
- * Components: _H2O_, _Air_
- * Fluid system: _TwoPTwoC_
+* Components: _H2O_, _Air_
+* Fluid system: _TwoPTwoC_
 
 ## Relevant headers
 
@@ -230,8 +285,8 @@ public:
 
 ## Example: 2 phases, miscible
 
- * Components: _CaO_, _CaO2H2_ (slaked lime)
- * Solid system: _OnePNCMin_
+* Components: _CaO_, _CaO2H2_ (slaked lime)
+* Solid system: _OnePNCMin_
 
 ## Specify solid system in properties file:
 
@@ -262,4 +317,4 @@ struct SolidSystem<TypeTag, TTag::ThermoChem>
 
 ## First step:
 
-Go to <https://git.iws.uni-stuttgart.de/dumux-repositories/dumux-course/tree/master/exercises/exercise-fluidsystem> and check out the README
+Go to [Fluidsystem exercise](https://git.iws.uni-stuttgart.de/dumux-repositories/dumux-course/-/tree/master/exercises/exercise-fluidsystem#exercise-fluidsystem-dumux-course)