  Helicity measures complexity in the field. Magnetic helicity is given by a
volume integral over the scalar product of magnetic field {\bf B} and its
vector potential {\bf A}. A direct computation of magnetic helicity in the
solar atmosphere is not possible due to unavailability of the observations at
different heights and also due to non-uniqueness of {\bf A}. The force-free
parameter $\alpha$ has been used as a proxy of magnetic helicity for a long
time. We have clarified the physical meaning of $\alpha$ and its relationship
with the magnetic helicity. We have studied the effect of polarimetric noise on
estimation of various magnetic parameters. Fine structures of sunspots in terms
of vertical current ($J_z$) and $\alpha$ have been examined. We have introduced
the concept of signed shear angle (SSA) for sunspots and established its
importance for non force-free fields. We find that there is no net current in
sunspots even in presence of a significant twist, showing consistency with
their fibril-bundle nature. The finding of existence of a lower limit of SASSA
for a given class of X-ray flare will be very useful for space weather
forecasting. A good correlation is found between the sign of helicity in the
sunspots and the chirality of the associated chromospheric and coronal
features. We find that a large number of sunspots observed in the declining
phase of solar cycle 23 do not follow the hemispheric helicity rule whereas
most of the sunspots observed in the beginning of new solar cycle 24 do follow.
This indicates a long term behaviour of the hemispheric helicity patterns in
the Sun. The above sums up my PhD thesis.
