The interest in investigating gravitational phenomena has risen in past few decades. A lot of them are out of the framework of the theory of general relativity, thus it is necessary to somehow modify this theory in order to find suitable mathematical description of unexplained phenomena.The class of symmetric teleparallel theories of gravity is one of the possible ways to modify the theory of general relativity. This class of theories describes the universe in the framework of metric-affine formalism on the manifold with zero independent curvature $R^\alpha{}_{\beta \mu \nu}$ and torsion $T^\alpha{}_{\mu \nu}$ and with nontrivial nonmetricity $Q_{\alpha \mu \nu}$. The first aim of this work is to explicitly describe the equations of motion in this class, including the process of receiving them from the action. The second aim is to analyze equations of motion in the specific theories of this class, including STERG, toy-model and the most promising $f(\cal{Q})$-model.