In these lecture notes I briefly discuss the present day situation and new discoveries in astrophysics of neutron stars focusing on isolated objects. The latter include soft gamma repeaters, anomalous X-ray pulsars, central compact objects in supernova remnants, the Magnificent seven, and rotating radio transients. In the last part of the paper I describe available tests of cooling curves of neutron stars and discuss different additional constraints which can help to confront theoretical calculations of cooling with observational data. 1