In an important sense writing a very short introduction to Christianity is virtually impossible. The books on Christianity in a University library run into thousands (with many on the New Testament, Contemporary Theology, the Crusades, Reformation, ethics, the Inquisition, patristics, martyrology, ecclesiology and so on); condensing this kind of information into a meaningful little book is an immense task as it involves a high degree of selection and omission; also, what is included is unlikely to receive much treatment; the Reformation, for example, has three and a half pages. Linda Woodhead manages to strike a good balance though whilst also raising relevant questions.
In discussing the significance of Jesus, she touches upon the synoptic problem and introduces the idea of there being many other 'gospels' of a more 'gnostic' or even feminist, nature. She also has very good discussions on the way that divine power is transmitted from God, through a male priesthood in the traditional types of Christianity (the theme of gender runs all through the book). Her main thesis is that Christianity can be braodly analysed into a typology of three types: Church Christianity, Biblical Christianity, and Mystical Christianty. This typology is helpful I think as it is hard to think of many traditions that fall entirely outside of it, though some will contain elements of all three.
Her section on gender is the most engaging I think as she discusses ways in which a traditionally male dominated religion might be attractive to women; all quite provocative.
Woodhead seems to have a very broad view of mysticism that even included Pentecostalism. I felt that this was quite far from the mark. Also, when discussing the Holy Spirit, she lapses into referring to the Spirit as 'it'. The concern is not whether or not the Spirit exists or whether she believes, it is simply not the way the Spirit is conceived to be within the tradition. She also says that for charismatics and pentecostals, salvation is sealed by the baptism of the Spirit and the reception of spiritual gifts; this is simply wrong; they accept all the fundamentals of an evangelical Church. But I want to praise the book, not bury it. It is an excellent introduction and really quite an achievement.