Megilas Taanis was a document which had written on it minor holidays which occurred during the second bais hamikdash. These were days that special things happened to klal yisrael.

All days on which it says we may not say a hespid [eulogy], the day before is also prohibited from saying a hespid, but the day after is permitted. R’ Yosee says both days are prohibited.

All days on which it says we may not fast, on the day before or after it is permitted to fast. R’ Yosee says the day before it is also prohibited but the day after it is permitted.

Taanis 2:9

The chachamim would not decree a fast day on the public at first so that prices would not shoot up. The first set of fasts was Monday Thursday Monday, the second set of fasts was Thursday Monday Thursday. R’ Yosee says all sets of fasts start on Monday.