## ABSTRACT

The work presented here is certainly not conclusive with respect to lattice algebra and its applications. We selected various lattices and theorems from Birkhoff's lattice theory that were needed for the mathematical foundation of lattice algebra. Thus, we had to forego discussing Borel lattices, σ-lattices, Boolean σ-algebras, von Neumann lattices, and many others. Considering applications, lattice algebra is at an extraordinary point in its development. Although the mathematical formulation of lattice theory and associated algebras began in the late 19th Century, their applications in other scientific fields started flourishing with the rise of the computer age. The number of researchers active in lattice-based applications has increased accordingly. These applications involve modeling methods, strategies, and procedures in a wide variety of scientific fields such as engineering, computer and information science, and applied mathematics. When surveying these widespread applications, one discovers a variety of different terminology and notations for the same objects, often causing some initial confusion.