  The epicenter of this paper concerns Pfister quadratic forms over a field $F$
with a Henselian discrete valuation. All characteristics are considered but we
focus on the most complicated case where the residue field has characteristic 2
but $F$ does not. We also prove results about round quadratic forms,
composition algebras, generalizations of composition algebras we call conic
algebras, and central simple associative symbol algebras. Finally we give
relationships between these objects and Kato's filtration on the Milnor
$K$-groups of $F$.
