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Introduction

This chapter is an introduction to the formalism of spectral sequences. We will be guided by three questions:
  1. What is a spectral sequence?
  2. What do we use them for?
  3. How do they arise?
The construction of spectral sequences from filtrations is taken up properly in later lectures; here we focus on the formal data, the language of pages, differentials, convergence, and a first computation with the Serre spectral sequence.