Literal Dyslexia: an individual facing difficulty in identification of letters, either unable to match sounds with the letters or unable to identify upper or lowercase letters.
Phonological Dyslexia: a person has difficulty with letters and connected sounds. They can read words that are familiar but have trouble reading unfamiliar words.
Neglect Dyslexia: a person neglects either side (letters to the left or right) of words - a problem particularly experienced in reading particularly words with too many characters.
Semantic Dyslexia: an individual distorting the meaning of a word or getting confused with the meaning that leads to incorrect reading.
Spelling Dyslexia: a person has problem reading any words and identifying individual letters.
Pure Dyslexia: a person having problem in reading only. There is no problem in writing.
Deep Dyslexia: a person has a problem in writing letters and words, grasping word-meanings, integrating the sounds of letters and in pronouncing less familiar words.
Note: Primarily dyslexia is of three types: Trauma, Deep and Developmental. Read more about them here. However, medical practitioners as well as people often classify dyslexia based on processing disorders. Other types of classifications are based on developmental reading approach. In this approach, dyslexia reading disorder is based on the concept of phonetics. Dyslexia falling under this category is more psychological in nature. Mainly there are three types of dyslexia: Dysphonetic, Dyseidetic and Dysphonetic/Dyseidetic.