  The fermionic von Neumann entropy, the fermionic entanglement entropy and the
fermionic relative entropy are defined for causal fermion systems. Our
definition makes use of entropy formulas for quasi-free fermionic states in
terms of the reduced one-particle density operator. Our definitions are
illustrated in various examples for Dirac spinors in two- and four-dimensional
Minkowski space, in the Schwarzschild black hole geometry and for fermionic
lattices. We review area laws for the two-dimensional diamond and a
three-dimensional spatial region in Minkowski space. The connection is made to
the computation of the relative entropy using modular theory.
