Quantum states hold fascinating properties that have stimulated innovative experiments in the fields ranging from precision metrology and interferometry to quantum communication, computing and cryptography. The ability to engineer, i.e. prepare, detect and measure arbitrary quantum states is thus, the holy grail of quantum information technology. This book reports a state-of-the-art quantum optical experiment capable of engineering arbitrary single-mode states containing only a few photons. All the desired states are remotely prepared in the ?signal? channel of a spontaneous parametric down conversion process by means of conditional measurements on the ?idler? channel. In view of light being the only possible physical system for ?decoherence free quantum communication? over long distances, the extension of control over the optical Hilbert space is a significant step. While this work should be of interest to any researcher in quantum optics and photonics, it would especially serve as a useful guide to graduate and senior undergraduate students doing experiments in quantum optical information science.