הודו להוי’ קראו בשמו Class One. Beginning of the Davening with a Minyan according to our custom. Half of Hodu is from one place (דברי הימים א’ ט”ז ח’ ואילך), the other half is from various Pesukim in Tehillim. The first half also is found almost identically in Tehillim 105. Hard to know when it was added to the Siddur but it is very old. It’s already mentioned in the מסכת סופרים and סדר עולם and others (but it’s not in RaMbaM). For the most part the Nusach is uniform, but some versions (Italian Nusach) are shorter. Some say it only on Shabbos and Yom Tov. The argument if it is said before ברוך שאמר (it is connected to Korbanos) or after (it is part of Pesukei DiZimra).
Class One הודו
הודו להוי’ קראו בשמו Class Two Inside read of the entire Hodu A division into parts, (not exact).
הודו להוי’ קראו בשמו וגו’ עלילותיו Class Three. This class is about the idea that in our Nusach, Hodu is the end of Asiya, the Hoda’a (submission and acceptance) stage, and not (like in Nusach Ashkenaz) the beginning of the Teva (Nature, Emotion) stage. We explore the four worlds and how they are in the four stages of Tefilla. The class finishes with about a half an hour of questions.
Class Three הודו
הודו להוי’ קראו בשמו וגו’ עלילותיו Class Four. The original הודו from דברי הימים is supplemented by more Pesukim representing what may not be so good. Hashem always saves even the sinners etc. The reasons for saying it: A) ארון הקדש the idea of שכינה and תורה B) קרבנות and the idea of Tefilla C) Thanking Hashem for for all the good D) Saving us from harm. If the reason for saying הודו is the ארון or קרבנות then it is said before ברוך שאמר, and if the reason for saying it is because Hashem helps us then it is said after ברוך שאמר.
Class Four הודו
הודו להוי’ קראו בשמו וגו’ עלילותיו Class Five. You can thank Hashem for what He gives you but you could also thank Him for the gift of (G-d) Himself. The reasons associated with the ארון and קרבנות are thanking Him for Himself. The difference between thanking Him for His presence (שכינה, the idea of Prophecy) and for the ability to approach Him (תפילה.) During Galus this is more complicated. The other reasons are thanking Him for what He does for us.