  In this thesis we consider two constructions generalizing the classical Arf
invariant. In the first construction an $\epsilon$-symmetric quadratic form
over a ring with involution $R$ is lifted to an $\epsilon(1+T)$-symmetric
quadratic form over the ring of formal power series $R[[T]]$ with involution
mapping $T$ to $\frac{-T}{1+T}$. The discriminant of this form can be viewed as
the classical Arf invariant $\omega_1$ of the original form, and the Hasse-Witt
invariant of this form gives rise to a `secondary' Arf invariant $\omega_2$,
which is defined on the kernel of $\omega_1$. The second construction yields an
invariant $\Upsilon$ which is defined on quadratic forms for which the
underlying symmetric form is standard. It takes values in a quotient of
quaternionic homology $HQ_1(R)$ which is defined using natural operations on
$HQ_1$. In the case of a commutative ring $\Upsilon$ agrees with
$(\omega_1,\omega_2)$. The invariant $\Upsilon$ is well suited for
computations. In particular we prove that it is faithful if $R$ is the group
ring over GF(2) of a group with two ends.
