  The main purpose of this work is to characterize derivations through
functional equations. This work consists of five chapters. In the first one, we
summarize the most important notions and results from the theory of functional
equations. In Chapter 2 we collect all the definitions and results regarding
derivations that are essential while studying this area.
  In Chapter 3 we intend to show that derivations can be characterized by one
single functional equation. More exactly, we study here the following problem.
Let $Q$ be a commutative ring and let $P$ be a subring of $Q$. Let $\lambda,
\mu\in Q\setminus\left\{0\right\}$ be arbitrary, $f\colon P\rightarrow Q$ be a
function and consider the equation \[ \lambda\left[f(x+y)-f(x)-f(y)\right]+
\mu\left[f(xy)-xf(y)-yf(x)\right]=0 \quad \left(x, y\in P\right). \] In this
chapter it will be proved that under some assumptions on the rings $P$ and $Q$,
derivations can be characterized via the above equation.
  Chapter 4 is devoted to the additive solvability of a system of functional
equations. Moreover, the linear dependence and independence of the additive
solutions $d_{0},d_{1},\dots,d_{n} \colon\mathbb{R}\to\mathbb{R}$ of the above
system of equations is characterized.
  Finally, the closing chapter deals with the following problem. Assume that
$\xi\colon \mathbb{R}\to \mathbb{R}$ is a given differentiable function and for
the additive function $f\colon \mathbb{R}\to \mathbb{R}$, the mapping \[
  \varphi(x)=f\left(\xi(x)\right)-\xi'(x)f(x) \] fulfills some regularity
condition on its domain. Is it true that in such a case $f$ is a sum of a
derivation and a linear function?
