The Bare Minimum

What you need to know to make sense of the later chapters in BS:

Realism: its MoM; its basic claims (shared by most members of the "family"), the particular claims of structural realism & of  neo-realism; the origins and consequences of the 'security dilemma'; some historical episodes of the practice of Realist principles; multiple meanings of the 'balance of power'; why Realists mistrust all forms of international organization as sources of security.  You should also be alert to the neo-realists' attachment to international regimes.

Marxism: its MoM; Marx' basic claims about how class struggle motivates development and change in human affairs; the particular extensions of Marx offered by Lenin (borrowing from Hilferding) and World System Theory, and a bit about Gramscian Marxist theory ('hegemony' of values); some historical episodes of Marxist (-inspired) statecraft and diplomacy; circumstances marking the end of the Cold War

Liberalism: its MoM: the claims of the four "images" of generations of Liberal thought; the role of the state in Liberal theory; 'collective security'; particular claims of Liberal Idealism; some historical episodes of the practice of Liberal principles (e.g., Woodrow Wilson's 14 Points); a bit about neo-liberal institutionalism.

Fortunately, our textbook is somewhat repetitious.  In later 'applied' chapters, the author will often restate or refer to the basic claims of the theory which he or she is applying.  So you'll re-read much of the content of Chapters 6-10.  However, later chapters don't try to give a coherent overview of the three theory-families.  No problem: you can turn back to the appropriate chapter to see how the pieces fit together.