The magnetization and the circular magnetic birefringence (CMB) or Faraday rotation φ
Fmeasurements in dysprosium iron garnet (DyIG) are reported in detail in the temperature range 2.6-300 K and under magnetic field H
aup to 26 kOe applied along either the easy axis |111| or the intermediate |110| direction. Typical linear field dependences of the magnetization and CMB are observed and their spontaneous values are obtained by extrapolating these evolutions to zero applied field. It is shown that the use of single crystals avoids the treatment adopted for polycrystalline samples by Pauthenet who extrapolated to infinite fields which may be doubtful. The anisotropic character of the magnetic properties and of the Faraday rotation appears to be very important below 100°K. The rare-earth contribution to the total CMB is determined and the field dependence of the total Faraday rotation is discussed from the paramagnetic evolution of the Dy
3+ions. Similar temperature evolutions are observed for the quantities χ
-1and

where χ is the magnetic susceptibility. Our experimental data, corresponding to these quantities, show some disagreement from the free ion Curie-Weiss\´s law as observed previously in polycrystalline samples. New values for the paramagnetic Curie temperature and the molecular field parameters of the Dy
3+sublattice are deduced from both the magnetic and magnetooptical data.