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This book introduces a new point-set level approach to stable homotopy theory that has already had many applications and promises to have a lasting impact on the subject. Given the sphere spectrum , the authors construct an associative, commutative, and unital smash product in a complete and cocomplete category of``-modules''whose derived category is equivalent to the classical stable homotopy category. This construction allows for a simple and algebraically manageable definition of``-algebras''and``commutative -algebras''in terms of associative, or associative and commutative, products . These notions are essentially equivalent to the earlier notions of $ A {\infty $ and $ E {\infty $ ring spectra, and the older notions feed naturally into the new framework to provide plentiful examples. There is an equally simple definition of -modules in terms of maps . When is commutative, the category of -modules also has a