  This paper is a part of a series of works where we in detail examine the
concept of Transverse Momentum Dependent (TMD), or k_T, factorization, which is
frequently encountered in the literature and is widely used in the
phenomenological applications of QCD at very high energies. We address the
question of what exactly factorization is, as it is meant in different contexts
and formalisms, and we compare the formalisms to each other. We clarify some
basic concepts regarding factorization and how it exactly is applied in high
energy QCD, and we make important notes on some key and fundamental points that
are often overlooked. We offer an extensive analysis of single inclusive
particle production, and we analyze the TMD gluon distribution that plays a
pivotal role in high energy QCD.
