In this chapter, we want to take a look at the mathematical concepts needed to describe four-dimensional curved spacetime. The required mathematical aids were essentially first researched by Bernhard Riemann (1826 – 1866) in the middle of the 19th century and were thus available to Einstein at the beginning of the 20th century. The theory developed by Riemann (the so-called differential geometry) is partly very abstract and “unwieldy”, so we choose a greatly simplified representation here, which omits many (mathematical) details and only briefly describes the essential constructs.