Chapter 1 contains some preliminary information on functional analysis, operator theory and complex analysis. The main results that will play the major role in the following chapters are concentrated in sections 1.7 and 1.8. They are rather technical, and I recommend to the reader who is interested mainly in differential equations to skip chapter 1 on the first reading. The statements of the main results of chapters 2-6 can be understood without referring to sections 1.7 and 1.8. The proofs, however, depend strongly on chapter 1. Chapter 2 provides the definitions and properties of transforms that play the role of the Fourier transform. Chapter 3 is devoted to the principal results of the Floquet theory for hypoelliptic equations. In chapter 4 it is shown how the Floquet theory is related to other properties of periodic equations (for instance, to spectral theory). Chapter 5 treats in more detail the case of evolution equations of hypoelliptic (in particular, parabolic) type. Writing this chapter, I found out that it was impossible to cover in one chapter even the case of time-periodic parabolic equations. I plan to give a more complete account of this topic in another publication. Chapter 6 contains a brief consideration of related problems: equations with deviating arguments, more general groups of periods, etc. Every chapter has a final section devoted to additional comments and references.