Number theory is the branch of mathematics that is primarily concerned with the counting numbers. Of particular importance are the prime numbers, the "building blocks" of our number system. The subject is an old one, dating back over two millennia to the ancient Greeks, and for many years has been studied for its intrinsic beauty and elegance, not least because several of its challenges are so easy to state that everyone can understand them, and yet no one has ever been able to resolve them. But number theory has also recently become of great practical importance.

The study of geometry is at least 2500 years old, and it is within this field that the concept of mathematical proof first arose. To this day geometry remains a very active area of research in mathematics. This Very Short Introduction covers the areas of mathematics falling under geometry, starting with topics such as Euclidean and non-Euclidean geometries, and ranging to curved spaces, projective geometry in Renaissance art, and geometry of space-time inside a black hole. Throughout, Maciej Dunajski outlines the role geometry plays in the broader context of science and art.

Physics, the fundamental science of matter and energy, encompasses all levels of nature from the subatomic to the cosmic, and underlies much of the technology around us. Understanding the physics of our universe is an essential aspect of humanity's quest to understand our environment and our place within it. Doing physics enables us to explore the interaction between environment and human society, and can help us to work towards the future sustainability of the planet.

Logic is often perceived as having little to do with the rest of philosophy, and even less to do with real life. In this lively and accessible introduction, Graham Priest shows how wrong this conception is. He explores the philosophical roots of the subject, explaining how modern formal logic deals with issues ranging from the existence of God and the reality of time to paradoxes of probability and decision theory. Along the way, the basics of formal logic are explained in simple, non-technical terms, showing that logic is a powerful and exciting part of modern philosophy.

In this Very Short Introduction audiobook, Richard Earl gives a sense of the more visual elements of topology (looking at surfaces) as well as covering the formal definition of continuity. Considering some of the eye-opening examples that led mathematicians to recognize a need for studying topology, he pays homage to the historical people, problems, and surprises that have propelled the growth of this field.

This short, smart book tells you everything you need to know about "nothing". What remains when you take all the matter away? Can empty space - "nothing" - exist? To answer these questions, eminent scientist Frank Close takes us on a lively and accessible journey that ranges from ancient ideas and cultural superstitions to the frontiers of current research, illuminating the story of how scientists have explored the void and the rich discoveries they have made there.

What is time? What does it mean for time to pass? Is it possible to travel in time? What is the difference between the past and future? Until the work of Newton, these questions were purely topics of philosophical speculation. Since then we've learned a great deal about time, and its study has moved from a subject of philosophical reflection to instead became part of the subject matter of physics.

Energy is vital for a good standard of living, and much of the world's population does not have enough. Affordable and adequate sources of power that do not cause climate change or pollution are crucial; and renewables provide the answer. Wind and solar farms can now provide the cheapest electricity in many parts of the world. Moreover, they could provide all of the world's energy needs.

India has a long, rich, and diverse tradition of philosophical thought, spanning some two and a half millennia and encompassing several major religious traditions. In this intriguing introduction to Indian philosophy, the diversity of Indian thought is emphasized. It is structured around six schools of thought that have received classic status. 

If you move at high speed, time slows down, space squashes up, and you get heavier. Travel fast enough and you could weigh as much as a jumbo jet, be flattened thinner than a CD without feeling a thing - and live forever! As for the angles of a triangle, they do not always have to add up to 180 degrees. And then, of course, there are black holes. These are but a few of the extraordinary consequences of Einstein's theory of relativity.

In this new edition, Steve Bruce discusses the continuing arguments for social egalitarianism, considering issues such as gay marriage, women in combat roles, and the 2010 Equality Act to debunk contemporary arguments against parity. As gender divisions are increasingly questioned, he looks ahead to the likely consequences of this for society.

Linguistics falls in the gap between arts and science, on the edges of which the most fascinating discoveries and the most important problems are found. Rather than following the conventional organization of many contemporary introductions to the subject, the author of this stimulating guide begins his discussion with the oldest, "arts" end of the subject and moves chronologically through to the newest research - the "science" aspects.

Rivers have acted as cradles for civilization and agents of disaster; a river may be a barrier or a highway, it can support trade and sediment, culture and conflict. This Very Short Introduction is a celebration of rivers in all their diversity. Geographer Nick Middleton covers a wide and eclectic range of river-based themes, from physical geography to mythology, to industrial history and literary criticism.

Games are everywhere: Drivers maneuvering in heavy traffic are playing a driving game. Bargain hunters bidding on eBay are playing an auctioning game. The supermarket's price for corn flakes is decided by playing an economic game. This Very Short Introduction offers a succinct tour of the fascinating world of game theory, a groundbreaking field that analyzes how to play games in a rational way. 

Quantum theory is the most revolutionary discovery in physics since Newton. This book gives a lucid, exciting, and accessible account of the surprising and counterintuitive ideas that shape our understanding of the sub-atomic world. It does not disguise the problems of interpretation that still remain unsettled 75 years after the initial discoveries. Uncertainty, probabilistic physics, complementarity, the problematic character of measurement, and decoherence are among the many topics discussed.