From: http://www.husserl.net/husserl/HusserlIntro.html
Edmund Husserl (1859-1938) was a philosopher best known for launching
phenomenology, the philosophical study of consciousness. Phenomenology
studies the world as it is given to or “constituted by” consciousness.
One can speak of the phenomenology of reading, of dancing, of mathematical
investigation, of chess-playing, and so forth, in each case meaning
an analysis or description of how that activity is experienced
by the person engaging in it (for example, the first-person experience
of dancing or playing chess). One can also study objects (construed
widely to include not just physical objects like tables and chairs
but also abstract objects like numbers and values) in terms of
the way they appear to consciousness. Husserl's philosophy was
notoriously complex. Among other things, Husserl sought to ground
all claims to knowledge in claims about consciousness, to introduce
a methodology for studying consciousness, to relate existing disciplines
(mathematics, logic, epistemology, psychology, natural science,
etc) to phenomenology, etc.