Pure alexia, also known as agnosic alexia or alexia without agraphia or pure word blindness, is one form of alexia which makes up "the peripheral dyslexia" group. Individuals who have pure alexia suffer from severe reading problems while other language-related skills such as naming, oral repetition, auditory comprehension or writing are typically intact.
Pure alexia results from cerebral lesions in circumscribed brain regions and therefore belongs to the group of acquired reading disorders, alexia, as opposed to developmental dyslexia found in children who have difficulties in learning to read.
Pure alexia almost always involves an infarct to the left posterior cerebral artery (which perfuses the splenium of the corpus callosum and left visual cortex, among other things). The resulting deficit will be pure alexia - i.e., the patient can write but cannot read (even what they have just written). However, because pure alexia affects visual input, not auditory input, patients with pure alexia can recognize words that are spelled out loud to them. This is because the left visual cortex has been damaged, leaving only the right visual cortex (occipital lobe) able to process visual information, but it is unable to send this information to the language areas (Broca's area, Wernicke's area, etc.) in the left brain because of the damage to the splenium of the corpus callosum. The patient can still write because the pathways connecting the left-sided language areas to the motor areas are intact. However, many people with pure alexia are able to identify and name individual letters over time as well as recognize sequences of letters as words. These people typically adapt to their disability and are able to use a style of compensatory reading known as letter-by-letter reading.  This style of reading takes longer than the conventional style of reading does. As the number of letters in a word increases, the amount of time it takes for the person with pure alexia increases. For each letter that is added, a patient may take up to an additional three seconds to read the word. 
Though there have been ample attempts to rehabilitate patients with pure alexia, few have proven to be effective on a large scale. Most rehabilitation practices have been specialized to a single patient or small patient group. At the simplest level, patients seeking rehabilitation are asked to practice reading words aloud repeatedly. This is meant to stimulate the damaged system of the brain. Another tactic that has been employed is the use of cross modal therapy. In this therapy, patients are asked to trace the words in which they are trying to read aloud. There has been success using cross modal therapy such as kinaesthetic or motor-cross cuing therapy, but tends to be a more feasible approach for those on the slower reading end of the spectrum. 
^Leff, Alexander P.; Schofield, T. M. "Rehabilitation of acquired alexia". International Encyclopedia of Rehabilitation. Center for International Rehabilitation Research Information and Exchange. Retrieved 30 March 2015.