This mograph is addressed to anyone interested in the subject of restrict- parameter-space estimation, and in particular to those who want to learn, or bring their kwledge up to date, about (in)admissibility and minimaxity problems for such parameter spaces. The coverage starts in the early 1950s when the subject of inference for - stricted parameter spaces began to be studied and ends around the middle of 2004. It presents kwn, and also some new, results on (in)admissibility and minimaxity for nsequential point estimation problems in restricted ?ni- dimensional parameter spaces. Relationships between various results are d- cussed and open problems are pointed out. Few complete proofs are given, but outlines of proofs are often supplied. The reader is always referred to the published papers and often results are clari?ed by presenting examples of the kind of problems an author solves, or of problems that cant be solved by a particular result. The mograph does t touch on the subject of testing hypotheses in - stricted parameter spaces. The latest books on that subject are by Robertson, Wright and Dykstra (1988) and Akkerboom (1990), but many new results in that area have been obtained since. The mograph does have a chapter in which questions about the existence of maximum likelihood estimators are discussed. Some of their properties are also given there as well as some algorithms for computing them. Most of these results cant be found in the Robertson, Wright, Dykstra book.