●1 QUASIGROUPS AND LOOPS 1.1 Latin squares 1.2 Equational quasigroups 1.3 Conjugates 1.4 Semisymmetry and homotopy 1.5 Loops and piques 1.6 Steiner triple systems I 1.7 Moufang loops and octonions 1.8 Triality 1.9 Normal forms 1.10 Exercises 1.11 Notes2 MULTIPLICATION GROUPS 2.1 Combinatorial multiplication groups 2.2 Surjections 2.3 The diagonal action 2.4 Inner multiplication groups of piques 2.5 Loop transversals and right quasigroups 2.6 Loop transversal codes 2.7 Universal multiplication groups 2.8 Universal stabilizers 2.9 Exercises 2.10 Notes3 CENTRAL QUASIGROUPS 3.1 Quasigroup congruences 3.2 Centrality 3.3 Nilpotence 3.4 Central isotopy 3.5 Central piques 3.6 Central quasigroups 3.7 Quasigroups of prime order 3.8 Stability congruences 3.9 No-go theorems 3.10 Exercises 3.11 Notes4 HOMOGENEOUS SPACES 4.1 Quasigroup homogeneous spaces 4.2 Approximate symmetry 4.3 Macroscopic symmetry 4.4 Regularity 4.5 Lagrangean prcperties 4.6 Exercises 4.7 Notes5 PERMUTATION REPRESENTATIONS 5.1 The category ]FSQ 5.2 Actions as coalgebras 5.3 Irreducibility 5.4 The covariety of Q-sets 5.5 The Burnside algebra 5.6 An example