The Moon is in synchronous rotation with the Earth so we always see the same side.  There are 8 lunar phases and they are caused by our view of the geometric relationship between the Sun, Moon and the Earth.  They are not caused by the shadow of the Earth cast upon the Moon.  The only time the Earth's shadow falls on the Moon is during a full or partial eclipse because of the 5 degree inclination with the Earth.  When the Moon is close to the horizon it appears larger than normal but that is just an optical illusion.  Lunar gravity affects our sea levels and the crime rate all over the world is higher during a Full Moon.  When we have a second Full Moon in a calendar month it is called a Blue Moon.  If given the chance, would you like to travel to the Moon?