Expressions like "John and Mary" or "the water in my cup" intuitively involve reference to collections of individuals or substances. The parthood relation between these collections and their components is not modeled in standard formal semantics of natural language (Montague 1974; Heim and Kratzer 1998), but it takes central stage in what is known as algebraic or mereological semantics (Link 1998; Krifka 1998; Landman 1996, 2000). This course provides a gentle introduction into the mathematical framework of classical extensional mereology, and is designed to help students understand important issues in the following problem domains, all of them active areas of research: plural, mass reference, measurement, aspect, and distributivity. In particular, the course shows how mereology sheds light on cross-categorial similarities between oppositions that pervade these domains, such as the count-mass, singular-plural, telic-atelic, and collective-distributive opposition. Students encounter issues involving natural language metaphysics and philosophy of language, and how these issues interact with semantic theory depending on how they are resolved. Much of the important seminal work in the area has been done in the 1980s and 1990s (e.g. Link, Krifka, Landman). More recently, significant new applications have cropped up, ranging from the influence of verbal semantics on cumulativity (e.g. Kratzer 2007) to the grammar of measurement (Schwarzschild 2006) to dependent plurals (Zweig 2009). The mereological perspective has kept opening up important new avenues for research across the decades (Kratzer 2007; Williams 2009). It has proven particularly useful in drawing out cross-categorial generalizations. Examples include recent work on pluractionality in Kaqchikel and its relation to group nouns (Henderson 2012), and my own work on a unified theory of distributivity, aspect and measurement (Champollion 2010). The mereological approach also provides a useful backdrop against which recent degree-semantic approaches to aspectual composition (Piñón 2008; Chris Kennedy 2012) and aspectual coercion (Deo and Piñango 2011) can be evaluated. In the first half of this course, I present introductions into algebraic semantics and selected applications involving plural, mass reference, measurement, aspect, and distributivity. I discuss issues involving ontology and philosophy of language, and how these issues interact with semantic theory depending on how they are resolved. The second half of this course develops strata theory, originally published in my dissertation (Champollion 2010) and essentially unchanged from that source. Lecture 8, on the scopal behavior of for-adverbials, is further elaborated on in Champollion (2013, 2014a). The latter paper also develops the theory of distributivity presented in Lecture 4. Lecture 9, on distance-distributivity, is based on Champollion (2012, 2014c).