Introduction; Terminology, conventions, and notation; Part I. Constructions, Examples, and Structure Theory: 1. Overview of pseudo-reductivity; 2. Root groups and root systems; 3. Basic structure theory; Part II. Standard Presentations and Their Applications: 4. Variation of (G', k'/k, T', C); 5. Universality of the standard construction; 6. Classification results; Part III. General Classification and Applications: 7. General classification and applications; 8. Preparations for classification in characteristics 2 and 3; 9. The absolutely pseudo-simple case in characteristic 2; 10. General case; 11. Applications; Part IV. Appendices: A. Background in linear algebraic groups; B. Tits' work on unipotent groups in nonzero characteristic; C. Rational conjugacy in connected groups; References; Index.