Galaxies are where stars live and die, and they are what we see when we look deep into the universe. Their nuclei often harbour supermassive black holes that can give rise to quasars and active galactic nuclei, which are some of the brightest objects in the universe. Galaxies form through the gravitational collapse of clouds of intergalactic matter. Small galaxies merge together to form larger ones, building up a rich hierarchy of structures in the process. The stars and active nucleii in galaxies interact with their environment by pervading it with radiation, by polluting it with heavy elements, and by driving supersonic winds into intergalactic space. These feedback processes are not well understood, but are thought to have profound consequences for the formation of subsequent generations of galaxies. Theoretical work on the formation of galaxies at Leiden includes both analytic modeling and large-scale computer simulations. Detailed study of the motions within galaxies allows us to deduce the strength of the gravitational field in galaxies, and hence their masses. These kinematic studies provide some of the best evidence for the existence of dark matter haloes in the universe. Using spectroscopy on the largest telescopes, such mass measurements can now be extended to higher and higher redshifts, allowing the evolution of galaxy masses to be observed. An independent technique is to use gravitational lensing (the deflection of light by gravitational fields) from ground- or space-based images. In nearby galaxies integral-field spectroscopy allows the kinematics to be measured over the face of the galaxy. The resulting maps can then be used to deduce fundamental properties such as intrinsic shape, overall mass, mass of the central black hole, rotation, and internal orbit structure of the galaxy. These in turn can be compared with the results from N-body simulations and orbit calculations to learn about the formation scenario of these galaxies, such as the merger history. The SAURON and PN.S instruments are examples of integral field spectrographs that are used to study galaxies. Our own Galaxy is the one that can be studied in most detail. It is the only place where star formation processes can be observed in close-up, and where the different stellar populations, that represent different episodes in the formation of the galaxy, can be separated cleanly. For stars in our Galaxy it is also possible to measure proper motions of stars, enabling three-dimensional velocities to be determined. The focus of these efforts is now on the GAIA satellite, which will measure velocity vectors for about 1 billion stars in the coming decade and hence provide the first really detailed look at the orbit distribution of stars in the Galaxy. A multi-wavelength approach to studying galaxies is fundamental. Much of the energy emitted by stars is absorbed by dust, and re-radiated in the far infrared. The dust absorption is much weaker in near-infrared light, so observations in this part of the spectrum are used to study obscured stellar populations, e.g. with the SINFONI instrument on the Very Large Telescope. The near-infrared is also important in the study of higher-redshift galaxies, most of whose starlight is redshifted out of the visible bands. To study high-redshift galaxies, the FIRES project has obtained the deepest near-IR pictures so far, using the VLT. Space observatories and ground-based sub-mm telescopes are used to study the dust-processed radiation, and so obtain a picture of the total energy balance of galaxies. Of particular interest are the 'SCUBA' sources, galaxies that are so dust-enshrouded that essentially all their optical starlight is absorbed. With radio telescopes the cold gas in galaxies can be studied, as well as the non-thermal radiation emitted near the nucleus. X-rays reveal the hottest gas. The outer parts of galaxies are usually too dilute to emit much radiation, but if there are bright sources, such as quasars, in the background, then they can be studied in great detail through the light it absorb from bright background sources such as quasars. Quasar absorption line studies currently provide some of the best constraints on the distribution and composition of matter in and around galaxies, particularly in the early universe.