The aim of this work is to discuss the effects found in static and dynamic wormholes that occur as a solution of Einstein equations in general relativity. The ground is prepared by presentation of "faster than light" effects, historical perspective, wormhole definition and contemporary directions in wormhole research. Then the focus is narrowed to Morris-Thorne framework for static spherically symmetric wormhole. Energy conditions being a fundamental component in wormhole physics are discussed in detail, their definition, most common violations and attempts to exotic matter quantification. Two types of dynamic wormholes, evolving and rotating, together with their variations are considered. Computer algebra and Cartan calculus are used to obtain detailed solutions. i Acknowledgement This thesis is a result of collaboration with my advisor, professor Nigel Bishop. I would like to use this opportunity to thank him for sharing his expertise, insight and many in depth discussions which have greatly enriched my understanding of applied mathematics. My appreciation extends to my family, Anna and Daniel, for their enthusiastic support, endless patience and help with day-today issues during this strenuous time. To my parents for their support of my choices even if they thought them to be too idealistic. Many words of special thanks belong to Elna whose energy, strong commonsense and help with meanders of English language are always highly valued and very much appreciated. To my friends and colleagues I would like to thank them for their tolerance and understanding of the fact that "gravity is what really matters" and accepting that this statement, can actually be elevated to a lifestyle, as in my case. I would also like to give many thanks to Unisa staff for the most fruitful relationship during a number of years and for making this university the most unique of its kind. v Notation We take the spacetime metric to have signature (− + ++) that is consistent with this of Misner, Thorne and Wheeler [79]. We shall use geometric units in which gravitational constant G and the speed of light c are set to one, when we deal with equations of general relativity. Latin indices are used to describe four dimensional expression i.e. a = 0, 1, 2, 3. Spacelike part of the expression is indexed by Greek characters i.e. α = 1, 2, 3. We denote components of Lorentzian metrics by η ab. In general the metric components are symbolized by g ab. vi