The last decade has witnessed amazing progress in our empirical and theoretical understanding of galaxy formation and evolution. This explosion in our understanding has been driven largely by technology: the profusion of 8-10-m class telescopes, the advent of wide-field multi-object spectrographs and imagers on large telescopes, servicing missions for the Hubble Space Telescope (HST), giving it higher resolution, higher sensitivity, larger field-of-view, and access to longer wavelengths, and the commissioning and/or launch of powerful observatories in the X-ray, ultraviolet, infrared, and sub-millimeter, are but a few of the important technological advances. This has led to a much-increased empirical understanding of broad phenomenologies: e.g., constraints on the overall shape of the cosmic history of star formation, the increased incidence of star-forming galaxies in less dense environments, the co-evolution of stellar bulges and the supermassive black holes that they host, and the increasing incidence of galaxy interactions at progressively higher redshifts, to name but a few. In turn, tension between these new observational constraints and models of galaxy formation and evolution have spurred on increasingly complex models, giving important (and sometimes predictive!) insight into the physical processes - star formation (SF), feedback, galaxy mergers, AGN activity - that are driving these phenomenologies.
In this review, I will give a grossly incomplete and biased overview of some hopefully interesting aspects of galaxy assembly. An important underpinning of this review is my (perhaps misguided) assumption that we live in a Universe whose broad properties are described reasonably well by the cold dark matter paradigm, with inclusion of a cosmological constant (CDM): m = 0.3, = 0.7, and H0 = 70 km s-1 Mpc-1 following results from the Wilkinson Microwave Anisotropy Probe ([Spergel et al. (2003)]) and the HST Key Project distance scale ([Freedman et al. (2001)]). This model, while it has important and perplexing fine-tuning problems, seems to describe detection of `cosmic jerk' using supernova type Ia ([Riess et al. (2004)]), and the evolving clustering of the luminous and dark matter content of the Universe with truly impressive accuracy on a wide range of spatial scales ([Seljak et al. (2004)]).
An important feature of CDM models in general is that galaxies are formed `bottom-up'; that is, small dark matter halos form first, and halo growth continues to the present through a combination of essentially smooth accretion and mergers of dark matter halos (e.g., [Peebles (1980)]). Thus, small halos were formed very early, whereas larger haloes should still be growing through mergers. This has the important feature of decoupling, to a greater or lesser extent, the physics and timing of the formation of the stars in galaxies, and the assembly of the galaxies themselves from their progenitors through galaxy mergers and accretion ([White & Rees (1978)]; [White & Frenk (1991)]).
Accordingly, in this review I strive to explore the two issues separately. First, I will explore the build-up of the stellar mass in the Universe, irrespective of how it is split up into individual galaxies. Then, I will move on to describing some of the first efforts towards understanding how the galaxies themselves assembled into their present forms. This article will not touch on many important and interesting aspects of galaxy evolution; the co-evolution (or otherwise) of galaxy bulges and their supermassive black holes (see, e.g., Peterson, these proceedings; [Ferrarese et al. (2001)]; [Haehnelt (2004)]), the important influences of local environment on galaxy evolution (see, e.g., [Bower & Balogh (2004)]), or the evolution of galaxy morphology (see, e.g., Franx, these proceedings). In this review, I adopt a CDM cosmology and a [Kroupa (2001)] IMF; adoption of a [Kennicutt (1983)] IMF in this article would leave the results unchanged.