Mark-recapture analysis of populations is becoming an important tool in population biology. Mark-recapture methods can be used to estimate transition probabilities among life-stages from capture histories of marked individuals for which stages can be determined at each sampling occasion. This method is called a multi-stage mark-recapture (MSMR) method. In this thesis, I describe advances I made in the MSMR method and present analyses that apply this method to actual data. The advances I made in the MSMR method are motivated by a need to provide a link between mark-recapture data and demographic models such as matrix population models and integrodifference models. I resolve some issues that are commonly encountered during sampling, such as the fact that the sex or life-stage of some individuals is unknown during some sampling occasions and that individuals become unobservable during some life-stages. I introduce a stage-structure that permits simple conversion of estimated transition probabilities into a matrix population model. I describe an algorithm to simplify programming for parameter estimation. I also introduce a method to estimate the distribution of dispersal displacements (a dispersal kernel) from mark-recapture data. I apply some of the methods described above to data of the North Atlantic right whale (Eubalaena glacialis). The right whales are considered one of the most endangered mammals. The current population size is about 300 in the northwestern Atlantic, and the number is declining. I applied the multi-stage mark-recapture statistics to the 17-year in- dividual sighting history data.