We show that the clusters formed by the irreversible aggregation of uniform aqueous gold colloids exhibit dilation symmetry and are well described as fractals with a Hausdorff or fractal dimension of ~1.75. The detailed structure of the clusters is studied with transmission electron microscopy, and is confirmed with small angle neutron scattering. The value of the fractal dimension obtained is in excellent agreement with that predicted by theory and computer simulation for cluster-cluster aggregation. We also discuss preliminary measurements of the kinetics of aggregation, which indicate that there are two limiting regimes with substantially different behavior. One is dominated by the particle-particle sticking time leading to relatively slow growth initially, but an increasing rate of growth as the aggregation proceeds. In contrast, the other is dominated by the diffusion time for clusters to collide leading to much faster aggregation, but with a decreasing rate of growth as the aggregation proceeds.