A normal year has 365 days. The first 6 months only have 181 days, while the last six months have 184 days. This means that on July 2 at noon you are exactly half way the year.
A Leap year has 366 days. The first and second quarter in such a year have 91 days, while the third en fourth quarter in a Leap year both have 92 days.
In the year 1582 the Julian Calendar (which had Leap years every four years) was replaced (at least in Roman Catholic countries) by the Gregorian Calendar. This calendar does not have Leap years in 1700, 1800, 1900, 2100, 2200... but still has Leap years in 1600, 2000, 2400... To be able to correct the error the Julian Calender introduced in its 16 centuries of existence, in October 1582, 10 days were skipped. In 1582, October 4 was followed by October 15.
The first century started in the year 1 AD, and because a century contains 100 years, it ended on December 31 of the year 100 AD. This means the 20th century in which we live started on January 1 of the year 1901 and it will end on December 31, 2000. Therefore, the next century starts in 2001!