The theory of electron correlation in semiconductor quantum dots is reviewed with emphasis on the physics of dots in strong magnetic fields. A brief survey of dot fabrication and experimental results is given, the quantum mechanics of small numbers of interacting electrons in a dot is discussed and the special values of angular momentum quantum number that the ground state is allowed to have, or magic numbers, are introduced. These numbers are selected because of the symmetry properties of the ground state and the symmetry is particularly evident in the limit of strong magnetic field if the system is examined in a moving reference frame. Physically, the system in this limit can be pictured as an electron molecule that rotates and vibrates in the dot, and this is the quantum dot analogue of a Wigner crystal. This is illustrated with a detailed treatment of a two-electron dot which can be studied without resorting to any special concepts of molecular physics. Next, the molecular physics concepts, such as the Eckart reference frame, needed to deal with rotational-vibrational motion of larger numbers of electrons are introduced. The physics of dots with more than two electrons is then described, including the evolution of magic numbers with electron number and the implications of symmetry. Finally, the extension of these ideas to larger systems and coupled dots is briefly discussed. Quantum dots in strong magnetic fields provide a unique opportunity to realize what could be called electron molecular physics, and some possible ways of probing the system experimentally are also proposed.

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