Contents -- 1. Assumed knowledge -- Preliminaries -- Fields -- Revision examples in linear algebra -- 2. Introduction -- The Desargues' and Pappus' configurations -- The extended Euclidean plane -- 3. Introduction to axiomatic geometry -- The extended Euclidean three-dimensional space -- The r-dimensional projective space S[sub(r)] -- Projective planes -- Order of a finite projective space -- Desargues' Theorem and non-Desarguesian planes -- 4. Field planes and PG(r,F) -- Preliminaries -- Field planes -- Three worked examples in PG(2, F) -- Homographies and collineations of planes -- Baer subplanes -- Singer's Theorem -- PG(r, F) -- PG(3, F) -- Cross-ratio and the harmonic property -- Correlations and polarities -- 5. Coordinatising a projective plane -- Preliminaries -- Introducing coordinates -- Addition in γ -- Multiplication in γ -- Hall Ternary Ring -- The Veblen-Wedderburn Ring -- 6. Non-Desarguesian planes -- (V, l)-perspectivities -- Group of elations -- (V, l)-transitive and (V, l)-Desarguesian planes -- The Hughes plane of order q[sup(2)], q an odd prime power -- The Hall planes -- 7. Conics -- Preliminaries -- Conics -- Conics over a finite field F of characteristic two -- Conics over fields of characteristic ≠ 2 -- Conic envelopes -- Conics over finite fields of odd characteristic -- Conics in PG(2, R) -- A non-empty irreducible conic viewed as a line -- Pencil and range of conics -- 8. Quadrics in PG(3, F) -- Preliminaries -- Quadrics Q[sup(2)][sub(2)] in PG(3, F) -- Hyperbolic and elliptic quadrics of PG(3, F) -- The twisted cubic -- Further Reading -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W.