Midrash Tehillim

The first (and earlier) part has much material dating back to the Talmudic period, although its final composition took place between the 7th and 9th centuries AD.

[11] But it cannot possibly be assumed that the aggadah collections on the Psalms are identical with the present Midrash Tehillim, since the latter contains many elements of later date.

Zunz assigned its definitive completion to the last centuries of the period of the Geonim, without attempting to determine an exact date.

Among the comments on single verses are many which are based on the difference of Qere and Ketiv, as well as on the variant spellings of words (plene and defective).

Many words, also, are explained according to the numerical value of the letters (gematria) or by analysis of their component parts (Noṭariḳon) as well as by the substitution of other vowels ("al-tiḳri").

[15] The midrash contains a number of stories, legends, parables, proverbs, and sentences, with many ethical and halakhic maxims.

Notable stories include that of Remus and Romulus, to whom God sends a she-wolf to suckle,[16] and the legend of Emperor Hadrian, who wished to measure the depth of the Adriatic Sea.

The author of this supplement was probably R. Mattithiah Yiẓhari of Zaragoza, who collected the scattered aggadot on Psalms 119-150 from the Yalkut Shimoni, adding comments of his own.