In my last post I dealt briefly with the way "faith" (and the related verb "I believe") is used in the Synoptic Gospels, and said I would deal with John's Gospel later.
In fact, the noun pistis ("faith") does not occur at all in John, although the verb pisteuo ("I believe") occurs nearly 100 times. It has been suggested (e.g. by R.T. France, et al) that the reason for this may well be that by the time John wrote his Gospel towards the end of the first century the noun had begun to be used to designate the body of Christian doctrine, whereas John was more interested in the relationship expressed by the verb form. Of course this is speculative, although it does fit in well with what we know of John.
One of things that is really interesting about John's use of pisteuo is that his most frequent usage is to write of belief/faith in/into Jesus (in fact only two cases refer to belief in God - all the rest are to belief in/into Jesus). R. T . France comments: "This is in striking contrast with the Synoptics usage ... where only one passage explicitly mentions believing in Jesus. While faith in the Synoptics is primarily faith in God and is directed principally toward the experience of miraculous power, in John it is faith in Jesus, and its focus is not on miracles and on the meeting of physical need, but on the establishment of a relationship which results in eternal life" (op cit). This must be read as similar to Paul's language about the incorporation of believers "into" the body of Christ so that they are "in Christ".
John has an interesting thing in common with the Synoptics: Jesus is never spoken of as believing in God. Jesus is the object, not the subject, of faith.