Learning Torah Before Prayers
It is forbidden for someone who prays alone to begin learning Torah once the time of Shacharit (Morning Prayers) arrives (dawn). This is due to a concern that he will become so involved in his learning that he will miss the time for reciting Shema and prayer. However, it is permitted to begin learning before dawn (Shulchan Aruch Orach Chaim 89:6). It is also permitted to learn if one appoints someone to remind him. (Mishneh Berurah)
One who already began to learn, even after dawn, is not required to stop as long as there will be enough time for him to pray afterwards. Some say that one who started learning after dawn must at least stop to recite Shema, while others do not require one to stop to say Shema unless there is a concern that the time for Shema will pass. (Mishneh Berurah)
One who will be going to pray in the Beit Knesset (and does so regularly) is allowed to learn Torah before praying, since in this case there is no concern that he will forget to pray. (Shulchan Aruch Orach Chaim 89:6)
Even someone who prays alone is allowed to teach others, since there is great merit in teaching Torah to others, and if he does not teach at that time they will lose out on the opportunity to learn (Shulchan Aruch ibid.). This is only allowed if the time for Shema will not pass while he is learning. If there is a concern that the time for Shema will pass he should recite Shema before beginning to learn (if the time of Shema has already arrived). (Mishneh Berurah)
The Kaf HaChaim explains that although the Shulchan Aruch forbids learning from dawn, since learning before praying is important one can follow the more lenient opinion that permits learning until sunrise nears (see Mishneh Berurah, who cites both opinions). The Piskei Teshuvot writes that people are not stringent about learning before prayers, and that anyone who finds it easier to learn before prayers based on his daily schedule may do so. He adds that according to the Mishneh Berurah and others there is almost no situation when it would be forbidden to learn before prayers. Of course, one must be careful to make sure not to miss the ideal times for Shema and prayer.