Let us start with a definition: by someone's handwriting we mean the way he writes, from a graphical point of view (in other terms, we are in no way interested into the contents).
Graphology is the discipline that aims to explore the writer's character based on his handwriting.

Graphology has a "prehistory" two millenia long, and over 120 years of sistematic research, brought on indepentently in different countries. This gave rise to several different methods — but one could say that its cradle is France.

Its applications are manifold:

Finally, there is the distinct but related field of forensic analysss of handwritted documents, like wills and testaments, signatures, anonymous letters, …

In any case, the graphologist need to have enough materials to work with — some extra-graphological informations are necessary too.