For our index to the commentaries on these chapters of Hallel, see the Mafteach to Tehilim section on our site, beginning here:

The Gemara says that the Nevi'im (Prophets) instituted that the Jewish people should recite Hallel for each "Perek" ("time period") at which they were saved, and for each "Tzarah" ("trouble") from which they were saved. What are the differences between these two types of Hallel?

How did Hashem prove His involvement in this lowly world, through the events of Yetzi'as Mitzrayim? What event in particular demonstrated this?