Part 1
Jews even outside Eress Yisrael kept only one day. So says Rashi. Tosafoth disagree. What makes the Jewish calendar different from the others? The advantage of relying on witnesses - and not a fixed calender - for the new moon.
Part 2
The Rambam says to keep one day of Rosh Hodesh in Eress Yisrael, but two days of Rosh haShannah. Why?
Part 3
Eress Yisrael kept one day for seven centuries, until outsiders forced them to change. Here's the proof.
Part 4
Does the fixed calendar change our practice or not? The logic behind keeping two days in Eress Yisrael today. How to decide between two major poskim. Tefillin during the second day.
Part 5
On a different issue, the Rambam rules according to popular practice, though here he does not.