The Golden Oldies series of the journal General Relativity and Gravitation reprints important papers in general relativity theory that were published 30 or more years ago and are either hard to get hold of, or were originally printed in a language other than English. They play a key part in making these important papers readily accessible today, in the language that has now become the lingua franca of scientific publication. The value of this reprinting is enhanced by an accompanying editorial note for each paper, which briefly explains the significance of the work and where it has subsequently led to, together with a biographical note about the author or authors. This volume presents a selection of 14 rarities among the Golden Oldies grouped in the three categories "Basic results in differential geometry and general relativity," "Discussion of physical effects" and "Basic exact solutions and their interpretation." Researchers in the field will appreciate having these important papers collected in one book for the first time. Reprinted from the journal General Relativity and Gravitation.

The Golden Oldies series of the journal General Relativity and Gravitation reprints important papers in general relativity theory that were published 30 or more years ago and are either hard to get hold of, or were originally printed in a language other than English. They play a key part in making these important papers readily accessible today, in the language that has now become the lingua franca of scientific publication. The value of this reprinting is enhanced by an accompanying editorial note for each paper, which briefly explains the significance of the work and where it has subsequently led to, together with a biographical note about the author or authors. This volume presents a selection of 14 rarities among the Golden Oldies grouped in the three categories "Basic results in differential geometry and general relativity," "Discussion of physical effects" and "Basic exact solutions and their interpretation." Researchers in the field will appreciate having these important papers collected in one book for the first time. Reprinted from the journal General Relativity and Gravitation.

Cosmology has been transformed by dramatic progress in high-precision observations and theoretical modelling. This book surveys key developments and open issues for graduate students and researchers. Using a relativistic geometric approach, it focuses on the general concepts and relations that underpin the standard model of the Universe. Part I covers foundations of relativistic cosmology whilst Part II develops the dynamical and observational relations for all models of the Universe based on general relativity. Part III focuses on the standard model of cosmology, including inflation, dark matter, dark energy, perturbation theory, the cosmic microwave background, structure formation and gravitational lensing. It also examines modified gravity and inhomogeneity as possible alternatives to dark energy. Anisotropic and inhomogeneous models are described in Part IV, and Part V reviews deeper issues, such as quantum cosmology, the start of the universe and the multiverse proposal. Colour versions of some figures are available at www.cambridge.org/9780521381154.

REDUCE is one of the most widely available and simple to use computer algebra systems. It enables users to manipulate complex algebraic expressions and equations symbolically just as mathematicians and scientists do traditionally on paper, and its capabilities include differentiation and exact symbolic integration. This book provides a comprehensive introduction to REDUCE from starting to run it through to using some of the user-contributed REDUCE packages written for specific applications. The authors' aim is to enable all students using REDUCE for the first time to gain a familiarity with the full range of REDUCE commands while at the same time learning something of the internal workings of REDUCE. Throughout, numerous exercises are provided to illustrate themes covered in the text as well as to encourage "hands on" working with REDUCE. Both authors are expert users of REDUCE and the text is based on their many years of teaching the system to undergraduate and graduate students. As a result, all those coming to use REDUCE for the first time will find this an invaluable tutor and guide. For more advanced users, it covers a number of aspects not included in the REDUCE manual.

Cosmology has been transformed by dramatic progress in high-precision observations and theoretical modelling. This book surveys key developments and open issues for graduate students and researchers. Using a relativistic geometric approach, it focuses on the general concepts and relations that underpin the standard model of the Universe. Part I covers foundations of relativistic cosmology whilst Part II develops the dynamical and observational relations for all models of the Universe based on general relativity. Part III focuses on the standard model of cosmology, including inflation, dark matter, dark energy, perturbation theory, the cosmic microwave background, structure formation and gravitational lensing. It also examines modified gravity and inhomogeneity as possible alternatives to dark energy. Anisotropic and inhomogeneous models are described in Part IV, and Part V reviews deeper issues, such as quantum cosmology, the start of the universe and the multiverse proposal. Colour versions of some figures are available at www.cambridge.org/9780521381154.

Integration of differential equations is a central problem in mathematics and several approaches have been developed by studying analytic, algebraic, and algorithmic aspects of the subject. One of these is Differential Galois Theory, developed by Kolchin and his school, and another originates from the Soliton Theory and Inverse Spectral Transform method, which was born in the works of Kruskal, Zabusky, Gardner, Green and Miura. Many other approaches have also been developed, but there has so far been no intersection between them. This unique introduction to the subject finally brings them together, with the aim of initiating interaction and collaboration between these various mathematical communities. The collection includes a LMS Invited Lecture Course by Michael F. Singer, together with some shorter lecture courses and review articles, all based upon a mini-programme held at the International Centre for Mathematical Sciences (ICMS) in Edinburgh.