In this paper we analyze algebra (operations and transformations) and geometry of the class of continuous piecewise linear functions (k -functions), in particular, their universal representativity and the algorithms reducing them from one representation to another. For the general piecewise linear programming problem, the dual is formed and the corresponding duality theorem is presented, the method of exact penalty function is grounded, and the saddle point theorems for the disjunctive Lagrangian are proved. It is noted that the logical part of algorithmic tools to solve k-problems can be implemented as a universal computer code allowing the formation and solution of the concluding family of standard linear programs, one of which gives the solution to the original k-problem.