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We calculate the low-lying glueball spectrum, some string tensions and someproperties of topology and the running coupling for SU(N) lattice gaugetheories in 3+1 dimensions. We do so for N = 2,3,...12, using latticesimulations with the Wilson plaquette action, and for glueball states in allthe representations of the cubic rotation group, for both values of parity andcharge conjugation. We extrapolate these results to the continuum limit of eachtheory and then to N=infinity. For a number of these states we are able toidentify their continuum spins with very little ambiguity. We calculate thefundamental string tension and k=2 string tension and investigate the Ndependence of the ratio. Using the string tension as the scale, we calculatethe running of a lattice coupling and confirm that g(a)**2 varies as 1/N forconstant physics as N->oo. We fit our calculated values of the string tensionwith the 3-loop beta-function, and extract a value for Lambda-MSbar, in unitsof the string tension, for all our values of N, including SU(3). We calculatethe topological charge Q for N=2,..,6 where it fluctuates sufficiently for aplausible estimate of the continuum topological susceptibility. We alsocalculate the renormalisation of the lattice topological charge, ZQ(beta), forall our SU(N) gauge theories, using a standard definition of the charge, and weprovide interpolating formulae, which may be useful in estimating therenormalisation of the lattice theta parameter. We provide quantitative resultsfor how the topological charge `freezes' with decreasing lattice spacing andwith increasing N, and show how we cicumvent this issue in our calculations.

SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology