Parton densities in quantum chromodynamics : gauge invariance path dependence and Wilson lines Particle number operators in quantum mechanics and in quantum field theory Geometry of quantum field theories Basics of Wilson lines in QCD Gauge invariant parton densities Simplifying Wilson line calculations The book consists of six chapters. In Introduction we briefly discuss the conceptual issues inherent to the theory of strong interaction in the high energy regime and present the motivation to the use of parton density functions within the QCD factorization framework. In Chapter 2 we introduce particle number functions in general form. We show how the normal time and path ordering operations make the multiple products of local quantum operators well defined and how Wicks theorems enable practical calculations of quantum correlation functions. Chapter 3 outlines geometrical approach to the construction of a general nonabelian gauge field theory. The idea of local gauge invariance is used to derive a Wilson line as a parallel transporter associated to field operators defined in different space time points. In Chapter 4 we give a detailed description of the properties of piecewise linear finite and infinite Wilson lines and present the basis for a new methodology of perturbative calculations with such Wilson lines. Chapter 5 is devoted to the principles of gauge invariant path dependent parton density functions (PDFs) which are intrinsic to QCD factorization approaches to the analysis of fully inclusive and semi inclusive hadronic processes at high energy. We discuss geometrical structure of the Wilson lines which make the PDFs gauge invariant paying special attention to the operator definition of transverse momentum dependent PDFs and their evolution