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Intro; Supervisor's Foreword; Abstract; Acknowledgements; Contents; 1 Integrability in the AdS/CFT Correspondence; 1.1 The AdS/CFT Conjecture; 1.2 Some Methods for Solving the Theory; 1.3 Integrability on the CFT Side; 1.4 Integrability on the String Theory Side; 1.5 Outline of the Thesis; References; Part I Integrability on the String Theory Side; 2 Strings in Coset Spaces; 2.1 Principal Chiral Model; 2.1.1 Basic Concepts. The Polyakov Action; 2.1.2 PCM Lagrangian and Integrability; 2.1.3 WZW Models; 2.1.4 Bosonic String Theory as a Coset Model
2.2 Supersymmetric String and Semi-symmetric Coset Model2.2.1 NSR and GS String Theories; 2.2.2 Superconformal Algebra; 2.2.3 Green-Schwarz String as a Coset Model; References; 3 Flux-Deformed Neumann-Rosochatius System; 3.1 Neumann-Rosochatius Systems in AdS5timesS5; 3.1.1 Neumann System; 3.1.2 Rosochatius System; 3.1.3 Neumann-Rosochatius System; 3.2 The Flux-Deformed Neumann-Rosochatius. Spinning Strings in mathbbRtimesS3; 3.2.1 Constant Radii Solutions; 3.2.2 Non-constant Radii Computations. Elliptic Strings; 3.3 Spinning Strings in AdS3; 3.3.1 Constant Radii Solutions
2.2 Supersymmetric String and Semi-symmetric Coset Model2.2.1 NSR and GS String Theories; 2.2.2 Superconformal Algebra; 2.2.3 Green-Schwarz String as a Coset Model; References; 3 Flux-Deformed Neumann-Rosochatius System; 3.1 Neumann-Rosochatius Systems in AdS5timesS5; 3.1.1 Neumann System; 3.1.2 Rosochatius System; 3.1.3 Neumann-Rosochatius System; 3.2 The Flux-Deformed Neumann-Rosochatius. Spinning Strings in mathbbRtimesS3; 3.2.1 Constant Radii Solutions; 3.2.2 Non-constant Radii Computations. Elliptic Strings; 3.3 Spinning Strings in AdS3; 3.3.1 Constant Radii Solutions