There are two separate accounts of creation in the book of Genesis. The first, which occupies the first chapter, describes the creation of the world, life, and humanity in the "7 Day" format. On the 6th day, God creates mankind, both male and female. In the second creation story which starts at Genesis 2:2 recounts the familiar story of Adam (a name which comes from the Hebrew for 'red earth' from which he was formed then given the breath of life), the creation of other life forms for Adam, and his dissatisfaction with these other life forms, which leads God to create Eve from taking Adam's rib out so she will be made from his same being.
In Jewish mythology the first creation story was said to speak of Adam and Lilith. This is vaguely mentioned in one of the Midrashim, but it mostly comes from apocryphal, or extra-biblical (as in, outside of the Bible) stories and texts. Lilith, historically, was a type of demon that was blamed for the deaths of infants and later was cast as a succubus (as can be seen in the Talmud). Of course, the idea of Adam having an original wife is one interpretation, and if one is going to accept both creation stories as inter-dependent, one could also argue that the male and female in the first chapter of Genesis is the Adam and Eve from the second chapter.
Modern historical-critical scholarship views the two creation stories as separate since, when read literally, they have discrepancies (some may say contradictions) in the order of creation, etc., and scholars note that one of the creation stories uses the term YHWH for God (sometimes written in the traditional German-scholarship interpretation as "Jehovah"), generally translated as LORD in capitals with the L being in larger font in most English translations, while the second creation story refers to God as Elohim, with God referencing himself in English translations with a plural pronoun as in "Let us make man in our image after our likeness" and others. There is a lot more to the debate than just this simple gloss, but you get the picture.
Believers who do not accept the critical interpretations of these academics, scholars, and linguists, note that the two stories differ in style: the first being a chronological account; whereas the second is a topical account. This rectifies the "differences in order of creation" between the two, by supplying the argument that God is merely presenting these life forms to Adam, not creating them at the time for him. The chronological/topical difference also rectifies the "male and female He created them"/Adam first then Eve discrepancy since Chapter two is an in depth analysis of the sixth day's brief overview. This reconciliation also accords with the traditional beliefs of some Jewish rabbis over the centuries (and of course of Christian literalists too). I hope that helps you out in knowing the different interpretations applied to these two critical chapters from various groups. This debate is a long and interesting one and further research and investigation is recommended for anyone interested in its many layers of meaning.