Physics is a Science of "unification", striving to find general fundamental principles that explain the largest possible extent of observed phenomena with the simplest set of physical laws. In this respect, electromagnetism is the standard theory that led to the unification of two important branches of physics: electricity and magnetism (its extension further led to the "standard model" of particle physics).
The theory is supported by Maxwell's equations, which read:
\begin{align} &\nabla\cdot\vec E=\frac{\rho}{\epsilon_0}\,, && \nabla\cdot\vec B=0\,,\\ &\nabla\times\vec E=-\partial_t\vec B\,, && \nabla\times\vec B=\mu_0\vec J+\mu_0\epsilon_0\partial_t\vec E\,. \end{align}
for $\vec E$ the electric field, $\vec B$ the magnetic field, $\rho$ the electric charge density and $\vec J$ the current density.