Phases of the Moon
The planet remains in the evening sky and sets down about 2 hours after Sun. Its brightness rises up to (-4.1) mag, which makes it far the brightest object in the south-western sky. You should have no problems to find it with naked eyes through the whole month.
Penumbral Lunar Eclipse
On January 10, there is a penumbral eclipse visible in Asia, Europe and Africa (except its most western part). However, the Moon is not moving through the dark shadow of the Earth (so called "umbra"), but only through its half-shadow (so called "penumbra"). The penumbra is the consequence of the refraction of light from Sun through the Earth's atmosphere. This type of eclipse is very hard to observe visually, because the difference in brightness between the eclipsed part and non-eclipsed part of the Moon's disc is very small indeed. In the perfect clear sky you can try to take digital photographs and then process them on the computer to see this difference.