The topics covered are: basic results on homogeneous approximation of real numbers in Chapter 1; the analogue for complex numbers in Chapter 4; basic results on non-homogeneous approximation in the real case in Chapter 2; the analogue for complex numbers in Chapter 5; fundamental properties of the multiples of an irrational number, for both the fractional and integral parts, in Chapter 3. Many proofs are offered here for the first time, although the results themselves are not novel.