The Rademacher symbol is algebraically expressed as a conjugacy class invariant quasimorphism PSL(2,ℤ)→ℤ yielding the bounded Euler class. I will explain (1) how, using continued fractions, it is realized as the winding number for closed curves on the modular surface around the cusp; (2) how, using Eisenstein series, one can naturally construct a Rademacher symbol for any cusp of a general noncocompact Fuchsian group; (3) and discuss some connections to arithmetic geometry.