"The Christian Life" are fragments of Barth's Church Dogmatics volume IV.4 (sections §§ 74, 76, 77 and 78) organized around the Lord's Prayer that Barth had not finished revising by the time he died in 1968. "The Christian Life" is not published with the rest of the 14 volume (or 31 volume paperback) set of the Church Dogmatics because Barth had not finished revising it. (The last volume in the set on the "Church Dogmatics" is the section § 75 on the doctrine of baptism from IV.4).
This was a required text book for the Fall 2010 Th.D. (Doctor of Theology) seminar at Duke Divinity School. It is a significant work which is quoted extensively in Barth's assistant Eberhard Busch's The Great Passion: An Introduction to Karl Barth's Theology and analyzed extensively in John Webster's Barth's Ethics of Reconciliation.
Eerdmans owns the American rights to this book and published a version in 1981.
Continuum books has the UK rights and reprinted the Eerdmans version in the UK in 2004.
"The Christian Life" is available at the Karl Barth Digital Library for people who have access to a library who has a subscription to that.