Torah study on Shabbat should be a joy and a pleasure. Therefore, some poskim advise against studying difficult and complicated subjects, because when one does not understand what he is studying he becomes tense and aggravated. Therefore, it is proper to review on Shabbat material that one already knows well or study clear and comprehensible material, everyone at their own level. Even Torah scholars should study easy material that does not require exertion on Shabbat (Or Zaru’a; Ya’avetz). Others maintain that, on the contrary, it is particularly appropriate for erudite individuals to delve into difficult passages (Maĥzik Berakha 290:6). It seems that there is no disagreement. Rather, it depends on the individual: one who enjoys raising difficulties and resolving them should study difficult passages, while one who likes understanding things clearly and straightforwardly should study material that is easier to grasp.
One should mainly study material that instructs one how to live life properly, as the Torah states: “Study them and observe them faithfully” (Devarim 5:1). Similarly, the poskim write that one who has limited time to spend studying Torah should devote it to learning halakha. He should also study matters of faith and morals so as to elevate his thoughts and improve his ways (MB 290:6; Derisha, Shakh, and Taz on YD §246; SAH, Talmud Torah 2:9). If this is the case even during the week, then on Shabbat one should certainly study Torah that will provide direction in life. For Shabbat is the inner essence of the week and is meant to illuminate and guide us during the six workdays. Each person needs to discern for himself what type of study, in addition to halakha, he finds most enlightening, be it theology, Tanakh, moralistic tracts, or Ĥasidut. Torah scholars who spend all week studying different areas of the Torah do not need these directives. They should learn whatever they want to learn.
It is good to come up with novel Torah ideas (ĥidushim) on Shabbat. Zohar (III 173:1) states that on Saturday night, after the neshama yeteira returns to heaven, God asks what ĥidushim each Jew innovated that Shabbat with the help of his neshama yeteira (Shlah, Masekhet Shabbat, Ner Mitzva §53). This does not refer to ĥidushim that require toil and pain, but those that make people happy and contain novel understandings of life. One who cannot create novel insights should learn something new (Maĥzik Berakha 290:5; Kaf Ha-ĥayim ad loc. 5).
One who has children should study Torah with them on Shabbat. This gives him a double mitzva. It is a mitzva for a father to teach his son Torah, as it says: “Teach them to your children” (Devarim 11:19). And the Sages state: “If one teaches his son Torah it is as if he has taught his son and his son’s son through all the generations, as it is written: ‘Make them known to your children and your children’s children’ (Devarim 4:9)” (Kiddushin 30:1). By teaching his son, he ensures that the Torah will continue to be transmitted from generation to generation until the end of time. The Sages further say that a grandfather who is privileged to teach his grandson Torah is akin to one who accepted the Torah at Mount Sinai, as the Torah states: “Make them known to your children and your children’s children,” which is immediately followed by “the day you stood before the Lord your God at Ĥorev” (Devarim 4:9-10). Since the Torah was given on Shabbat, it is a particularly appropriate time to transmit the Torah.