  Form methods give a very efficient tool to solve evolutionary problems on
Hilbert space. They were developed by T. Kato [Kat] and, in slightly different
language by J.L. Lions. In this expository article we give an introduction
based on [AE2]. The main point in our approach is that the notion of
closability is not needed anymore. The new setting is particularly efficient
for the Dirichlet-to-Neumann operator and degenerate equations. Besides this we
give several other examples. This presentation starts by an introduction to
holomorphic semigroups. Instead of the contour argument found in the
literature, we give a more direct argument based on the Hille--Yosida theorem.
