Explore the intriguing world of ball quotients and their connections to algebraic geometry in this comprehensive lecture. Delve into the fascinating realm of moduli spaces in algebraic geometry, focusing on those with Kaehler metrics of constant negative holomorphic curvature. Examine how these spaces can be identified with Zariski open subsets of complex ball quotients through period maps. Investigate Allcock's groundbreaking discovery of a 13-dimensional ball quotient and its potential links to sporadic finite simple groups, including the Monster group. Review significant examples of ball quotients with modular interpretations, concentrating on those of dimension 10 or less. Conclude by exploring recent advancements in understanding the 'moonshine properties' of Allcock's ball quotient, shedding light on its mathematical significance and potential applications in the field.