This book is organized around the distinction between finite and infinite. It includes a brief overview of what different philosophers have said about infinity, and looks at some of the arguments to the effect that one should adopt a pro-infinity attitude. Other chapters contain an exposition of the ontological 'schools'; interactions among these schools and various theories of truth; the relationship between mathematics and values; a history of mathematics; an analysis of mathematical knowledge in terms of some traditional epistemological distinctions; the role of mathematics in education; the implications of religion for the philosophy of mathematics; and finally, reference to mathematical objects. This is a non-technical overview of the central issues in the Philosophy of Mathematics, an insightful but broad picture.