After reviewing the standard uncertainty relations due to Heisenberg (1927), Robertson (1929), and Schrodinger (1930), as well as the relations of Deutsch, and of Maassen and Uffink-including the so-called entropic relations-the author presents a complete account of the uncertainty relationship between complementary aspects in terms of superspace geometry, an approach not hitherto employed. Two incompatible properties A= Sigma alpha Aalpha mod alpha )( alpha mod and N= Sigma nNn mod n)(n mod belong to a pair of complementary aspects defined by two orthonormal bases ( mod alpha )) and ( mod n)) in the Hilbert space H. If the state is mod psi >, then P( alpha )= mod ( alpha mod psi ) mod 2 is the probability of obtaining the value Aalpha in a measurement of A, and P(n)= mod (n mod psi ) mod 2 is the probability of obtaining the value Nn in a measurement of N. The two aspects are characterised, relative to mod psi ), by the numbers (so-called purities): pi = Sigma alpha P( alpha )2 and pi = Sigma n P(n)2, both <or=1. He gives a complete characterisation of the uncertainty relationship between A and N (more precisely: between their aspects) in terms of the range of joint values of ( pi , pi ) for arbitrary initial states (pure as well as mixed). A theorem of Lenard is given an alternative proof, employing only elementary (superspace) geometry. The results depend on two angles, phi m=minimal angle, and phi M=maximal angle between the two aspects. Exact expressions for phi m and phi M are obtained in terms of the overlap matrix Lambda =( Lambda alpha n)=( mod ( alpha mod n) mod 2). As a corollary he finds the uncertainty relation for a pure state mod psi ) pi + pi <or=1+1/g+1-1/g cos phi m (where g=dim H), and a sharper one for mixed states. pi + pi =2 is obtainable if and only if the intersection of the aspects holds a pure state. If phi m= pi /2 (maximal incompatibility), then pi + pi <or=1+1/g is a special case of a stronger relation: Sigma mu g=o pi ( mu )=2, which one obtains for g+1 maximally incompatible aspects by means of a thereom of Ivanovic.