1 Introduction.- 1.1. Conspectus, 1; 1.2. Evolution of jaws, 2; 1.3. Fossil record, 4; 1.4. Environment, 6; 1.5. Classification, 7; References, 8; Bibliography, 9..- 2 Class Cephalaspidomorphi.- 2.1. Classification, 10; 2.2. Cephalaspidomorph characteristics, 11; 2.3. Infraclass 1, Osteostraci, 12; 2.3.1. Structure, 13; 2.3.2. Growth and life history, 19; 2.3.3. Diversity and tendencies in evolution, 20; 2.4. Infraclass 2, Anaspida, 23; 2.4.1 Structure, 24; 2.4.2. Growth, 26; 2.4.3. Diversity, 27; 2.5. Infraclass 3, Petromyzonida, 27; 2.5.1. Structure, 27; 2.6. Incertae sedis Palaeospondylus, 28; 2.7. Mode of life, 29; References, 31..- 3 Class Pteraspidomorphi.- 3.1. Classification, 35; 3.2. Pteraspidomorph characteristics, 36; 3.3. Subclass 1, Heterostraci, 36; 3.3.1. Structure, 36; 3.3.2. Growth and the evolution of the shield, 41; 3.3.3. Diversity and interrelationships, 45; 3.3.4. Mode of life, 49; 3.4. Incertae sedis Polybranchiaspis, 52; 3.5. Subclass 2, Thelodonti, 53; 3.5.1. Structure, 53; 3.5.2. Diversity and affinities, 55; 3.6. Relationships of agnathans, 56; References, 57..- 4 Subclass Acanthodii.- 4.1. Classification, 61; 4.2. Acanthodian characteristics, 61; 4.2.1. Structure, 63; 4.2.2. Diversity and tendencies in evolution, 71; 4.2.3. Mode of life, 75; References, 76..- 5 Subclass Osteichthyes. Infraclass Actinopterygii.- 5.1. Classification, 79; 5.2. Osteichthyan characteristics, 80; 5.3. Infraclass Actinopterygii, 81; 5.4. Superorder 1, Chondrostei, 86; 5.5. Order 1, Palaeoniscida, 86; 5.5.1. Structure, 87; 5.5.2. Suborder 1, Palaeoniscoidei, 91; 5.5.3. Suborder 2, Platysomidei, 94; 5.6. Order 2, Haplolepidida, 97; 5.7. Order 3, Tarrasiida, 97; 5.8. Order 4, Phanerorhynchida, 98; 5.9. Order 5, Dorypterida, 99; 5.10. Superorder 2, Holostei, 99; 5.11. Order 1, Semionotida, 100; 5.12. Tendencies in evolution, 102; References, 105..- 6 Subclass Osteichthyes. Infraclass Crossopterygii.- 6.1. Classification, 110; 6.2. Crossopterygian characteristics, 111; 6.3. Superorder 1, Rhipidistia, 113; 6.3.1. Structure, 114;6.3.2. Order 1, Holoptychiida, 122; 6.3.3. Order 2, Osteolepidida, 125; 6.3.4. Order 3, Rhizodontida, 126; 6.3.5. Tendencies in evolution, 127; 6.4. Superorder 2, Actinistia, 127; 6.4.1. Structure, 127; 6.4.2. Diversity, 131; 6.5. Incertae sedis Onychodontidae, 131; 6.6. Mode of life, 134; References, 136..- 7 Subclass Osteichthyes. Infraclass Dipnoi.- 7.1. Classification, 141; 7.2. Dipnoan characteristics, 141; 7.3. Structure and diversity, 144; 7.3.1. Structure, 144; 7.3.2. Diversity, 149; 7.4. Evolution and mode of life, 153; 7.5. Growth of cosmoid scales and bones, 154; 7.6. R elationships of teleostomes, 155; References, 158..- 8 Subclass Placodermi.- 8.1. Classification, 161; 8.2. Placoderm characteristics, 162; 8.3. Order 1, Arthrodira, 163; 8.3.1. Structure, 164; 8.3.2. Diversity and tendencies in evolution, 170; 8.4. Order 2, Ptyctodontida, 178; 8.5. Order 3, Phyllolepidida, 180; 8.6. Order 4, Petalichthyida, 181; 8.7. Order 5, Rhenanida, 185; 8.7.1. Suborder 1, Palaeacanthaspidoidei, 185; 8.7.2. Suborder 2, Gemuendinoidei, 188; 8.8. Order 6, Antiarchi, 191; 8.9. Incertae sedis Stensioellidae, 195; 8.10 Evolution and mode of life, 197; References, 200..- 9 Subclass Chondrichthyes. Infraclass Elasmobranchii.- 9.1. Classification, 206; 9.2. Chondrichthyan characteristics, 206; 9.3. Infraclass Elasmobranchii, 209; 9.4. Order 1, Cladoselachida, 210; 9.5. Order 2, Cladodontida, 213; 9.6. Order 3, Selachii, 215; 9.6.1. Suborder 1, Ctenacanthoidei, 215; 9.6.2. Suborder 2, Hybodontoidei, 217; 9.7. Order 4, Xenacanthida, 218; 9.8. Incertae sedis Order 5, Helicopriondia, 220; 9.9. Evolution, 221; 9.10. Mode of life, 222; References, 223..- 10 Subclass Chondrichthyes. Infraclass Holocephali.- 10.1. Classification, 226; 10.2. Holocephalan characteristics, 227; 10.3. Order 1, Chimaerida, 229; 10.3.1. Suborder 1, Helodontoidei, 229; 10.3.2. Suborder 2, Cochliodontoidei, 231; 10.3.3. Suborder 3, Menaspoidei, 231; 10.4. Order 2, Chondrenchelyida, 233; 10.5. Order 3, Edestida, 234; 10.6. Incertae sedis Ornithoprion, 237; 10.7. Order 4, Psammodontida, 238; 10.8. Order 5, Copodontida, 238; 10.9. Incertae sedis Order 6, Petalodontida, 239; 10.10 Evolution and mode of life, 240; 10.11. Relationship of elasmobranchiomorphs, 242;References, 244..- 11 Summary of the early evolution of fishes.