  Solar activity is controlled by the magnetic field, which also causes the
variability of the solar irradiance that in turn is thought to influence the
climate on Earth. The magnetic field manifests itself in the form of structures
of largely different sizes. This thesis concentrates on two types of the
smallest known magnetic features: The first part studies the properties of
umbral dots, dot-like bright features in the dark umbra of a sunspot. The
obtained umbral dot properties provide a remarkable confirmation of the results
of recent magneto-hydrodynamical simulations. Observations as well as
simulations show that umbral dots differ from their surroundings mainly in the
lowest photospheric layers, where the temperature is enhanced and the magnetic
field is weakened. In addition, the interior of the umbral dots displays strong
upflow velocities which are surrounded by weak downflows. This qualitative
agreement further strengthens the interpretation of umbral dots as localized
columns of overturning convection. The second part of the thesis investigates
bright points, which are small-scale brightness enhancements in the darker
intergranular lanes of the quiet Sun produced by magnetic flux concentrations.
Observational data obtained by the balloon-borne solar telescope SUNRISE are
used in this thesis. For the first time contrasts of bright points in the
important ultraviolet spectral range are determined. A comparison of
observational data with magneto-hydrodynamical simulations revealed a close
correspondence, but only after effects due to the limited spectral and spatial
resolution were carefully included. 98% of the synthetic bright points are
found to be associated with a nearly vertical kilo-Gauss field.
