The abstract version of the Lefschetz fixed point theorem is proved which states the following: If \(X\) is a metric space and if \(X_0\subset X\) is such that \(X_0\) absorbs compact sets, \(f\:X\to X\) is a continuous map, \(f(X_0) \subset X_0\) and \(f/X_0\) is a Lefschetz map, then \(f\) is also (on \(X\)) a Lefschetz map. Here a continuous map \(f\:X\to X\) is called a Lefschetz map if the generalized Lefschetz number \(\Lambda (f)\) of \(f\) is well defined and \(\Lambda (f) \neq 0\) implies that the set Fix\((f)\neq 0\). From that theorem three relative versions of the Lefschetz fixed point theorem are deduced which are connected with condensing and \(k\)-set contraction mappings.