Definitions of analysis:

noun: an investigation of the component parts of a whole and their relations in making up the whole
noun: the abstract separation of a whole into its constituent parts in order to study the parts and their relations
noun: a branch of mathematics involving calculus and the theory of limits; sequences and series and integration and differentiation
noun: a form of literary criticism in which the structure of a piece of writing is analyzed
noun: the use of closed-class words instead of inflections: e.g., `the father of the bride' instead of `the bride's father'
noun: a set of techniques for exploring underlying motives and a method of treating various mental disorders; based on the theories of Sigmund Freud
Example: "His physician recommended psychoanalysis"