  The aim of this article is to give a concise algebraic treatment of the
modular symbols formalism, generalised from modular curves to Hecke triangle
surfaces. A sketch is included of how the modular symbols formalism gives rise
to the standard algorithms for the computation of holomorphic modular forms.
Precise and explicit connections are established to the cohomology of Hecke
triangle surfaces and group cohomology. In all the note a general commutative
ring is used as coefficient ring in view of applications to the computation of
modular forms over rings different from the complex numbers.
  This is a "stack-free" version of Chapter 2 of my thesis.
