Women, [1] in regards to reciting and touching the Quran can be classified into five categories:

1)    When she is free from menses and lochia/postnatal bleeding

2)   When she is menstruating

3)   When she is menstruating while in the state of major impurity/janābah

4)   When she completes her menses before performing the ritual  washing/ghusl

5)   When she in bleeding from lochia

As for the first, it is permissible for her to recite the Quran whether or not she is in the state of ablution[2]

As for touching the Quran:

-If she is in the state of ablution it is permissible to touch the Quran

-If she is not in the state of ablution she is not permitted to touch the Quran (unless she is teaching or studying it then it is permissible as a dispensation due to the difficulty of always having to maintain ablution)  

As for the second, it is permissible for her to recite the Quran.

The primary rule is that it is not permissible, but a dispensation is granted in this case because she has no ability to remove her state of impurity.

As for touching the Quran:

If she is teaching or learning it then it is permissible

-If she is not doing either of the two then it is prohibited[3]  

As for the third, the scholars of the school differed whether or not she is permitted to recite Quran.

The relied upon opinion/ al-mu’tamid in the school is that she is permitted. Those who permit it give preference to the dispensation of difficulty, which is granted due to the impossibility of removing the state of ritual impurity. Those who do not permit it give preference to her being in the state of major impurity/janabah which prohibits the reciting of Quran.

As for touching the Qur’an, she is not permitted.  

As for the fourth, the scholars of the school differed whether she can recite the Quran or not.

The relied upon opinion is that she is not permitted to recite the Quran in this case because after her menses is complete she has the ability to remove her state or major ritual impurity  and so the dispensation will not apply.

As for touching the Quran it is not permissible.  

As for the fifth, she takes the same rule as a woman in menstruation according to some scholars.

NOTE:

It is permissible under all circumstances for any person, male or female, to recite a few verses of the Qur’an, whether in minor or major states of impurity, for the following purposes:

-Seeking refuge from shaytan (ex. reciting Surah Al-Nass, Al-Falaq or a Verse such as Ayatul Al-Kursi)

-Medical treatment through Quran recitation /ruqyah

-Reciting a few verses for the sake of providing a scriptural proof from the Quran.

[1] The word “women” is being used here as opposed to “female” to rule out young girls before the again of puberty. This article focuses on issues concerning menses and lochia, which do not include females before the age of puberty.
[2] Note that in this article the rule of reciting the Quran is mentioned first in each section. Thereafter, the rule of touching the Quran follows.
[3] The determining factor here is intention. Thus, if her intention is to learn, the dispensation will apply. On the other hand, if she intends simply to read for some type of reward or spiritual benefit, the dispensation will not apply.
source: http://www.al-masalik.com/y4uld/