  In this paper we consider Idempotent Functional Analysis, an `abstract'
version of Idempotent Analysis developed by V. P. Maslov and his collaborators.
We give a review of the basic ideas of Idempotent Analysis. The correspondence
between concepts and theorems of the traditional Functional Analysis and its
idempotent version is discussed; this correspondence is similar to N. Bohr's
correspondence principle in quantum theory.
  We present an algebraical approach to Idempotent Functional Analysis. Basic
notions and results are formulated in algebraical terms; the essential point is
that the operation of idempotent addition can be defined for arbitrary infinite
sets of summands. We study idempotent analogs of the main theorems of linear
functional analysis and results concerning the general form of a linear
functional and scalar products in idempotent spaces.
