This thesis deals with relativistic membranes and, in particular, a limit called stretched membranes. The thesis also considers the relation of membranes to the conjectured M-theory and string theory. The thesis is divided into two parts. One introductory part where I introduce areas which are of relevance for the second part.

The second part consists of the scientific papers.

In the first part I make a general introduction to string theory. Furthermore, I discuss different limits of membrane theory. Then, I make a short review of the different conjectures of M-theory and briefly mention different consistency checks of these conjectures. The last subject in the first part concerns an area, which is not

in direct connection to the other chapters in the thesis. This is a short introduction to the general treatment of theories with constraints.

The second part of the thesis consists of the included articles. The common topic of these is that they give a new approach to the treatment of membranes. We here make a partial gauge-fixing of the constraints which, by choosing an appropriate limit, will yield a perturbation theory around a free string-like theory. The stringlike

theory is the usual string theory with an extra parameter dependence. This perturbation theory we solve by infinitesimal canonical transformations.

The corresponding quantum theory is also discussed. We show that a particular ordering gives critical dimensions 27 and 11 for the bosonic and fermionic case respectively.