Word for "reading carefully"

Solution 1:

The closest you're likely to get in a single word is peruse.

Solution 2:

Close reading describes, in literary criticism, the careful, sustained interpretation of a brief passage of text. Such a reading places great emphasis on the particular over the general, paying close attention to individual words, syntax, and the order in which sentences and ideas unfold as they are read.

Slow reading is the intentional reduction in the speed of reading, carried out to increase comprehension or pleasure. The concept appears to have originated in the study of philosophy and literature as a technique to more fully comprehend and appreciate a complex text. More recently, there has been increased interest in slow reading as result of the slow movement and its focus on decelerating the pace of modern life.

For single word alternatives, you would simply study a text.