Summary: Certain elementary properties of the theory of least squares are presented from the point of view of complex stochastic processes. The development parallels the real case. We consider the least squares estimate (LSE), the best linear unbiased estimate (BLUE), the Markov estimate (ME), and the relationships among them. In particular, we prove the Gauss-Markov theorem and give necessary and sufficient conditions that the LSE and ME be identical. The efficiency of the LSE is defined and a lower bound is obtained for the efficiency of a certain class of models. Estimation of the mean vector and variance for a complex normal population leads to the maximum likelihood estimates (MLE). We prove that the MLE of the mean vector is identical with the LSE, and deduce other analogous properties concerning the distribution of the MLE.