Here's what the Holy Women, Holy Men website says about Barth:
Born in Switzerland in 1886, Barth studied at several prestigious universities including Tübingen. After completing his studies, he served as pastor in Geneva and Safenwil. The events of the First World War led Barth to critically question the dominant theology of the day, which, in Barth’s view, held a too easy peace between theology and culture. In his Commentary on Romans, published in 1918, Barth reasserted doctrines such as God’s sovereignty and human sin, central ideas which he believed were excluded and overshadowed in theological discourse at that time.
With Hitler’s rise to power, Barth joined the Confessional Church and was chiefly responsible for the writing of the Barmen Declaration (1934), one of its foundational documents. In it, Barth claimed that the Church’s allegiance to God in Christ gave it the moral imperative to challenge the rule and violence of Hitler. Barth was himself ultimately forced to resign his professorship at Bonn due to his refusal to swear an oath to Hitler. In 1932, Barth published the first volume of his thirteen-volume opus, the Church Dogmatics. Barth would work on the Dogmatics until his death in 1968. An exhaustive account of his theological themes and a daring reassessment of the entire Christian theological tradition, the Dogmatics gave new thought to some of the central themes first articulated in the Commentary on Romans. In the first volume, "The Doctrine of the Word of God," Barth laid out many of the theological notions which would comprise the heart of the entire work, including his understanding of God’s Word as the definitive source of revelation, the Incarnation as the bridge between God’s revelation and human sin, and the election of the creation as God’s great end.
Karl Barth was one of the great thinkers of the twentieth century. Pope Pius XII regarded him as the most important theologian since Thomas Aquinas. This assessment speaks to the respect Barth received from both Protestant and Catholic theologians and to his influence within both theological communities.
Here are some quotes from Barth I found online (I'm not sure about the original sources for them):
"Jesus does not give recipes that show the way to God as other teachers of religion do. He is himself the way."
"In the Church of Jesus Christ there can and should be no non-theologians."
"Jews have God's promise and if we Christians have it, too, then it is only as those chosen with them, as guests in their house, that we are new wood grafted onto their tree."
"Man can certainly flee from God, but he cannot escape him. He can certainly hate God and be hateful to God, but he cannot change into its opposite the eternal love of God which triumphs even in his hate."
"Faith in God's revelation has nothing to do with an ideology which glorifies the status quo."
"All sin has its being and origin in the fact that man wants to be his own judge. And in wanting to be that, and thinking and acting accordingly, he and his whole world is in conflict with God. It is an unreconciled world, and therefore a suffering world, a world given up to destruction."
"No one can be saved - in virtue of what he can do. Everyone can be saved - in virtue of what God can do."
And here's an excerpt from Barth's Church Dogmatics:
Jesus was not in any sense a reformer championing new orders against the old ones, contesting the latter in order to replace them by the former. He did not range Himself and His disciples with any of the existing parties. One of these, and not the worst, was that of the Pharisees. But Jesus did not identify Himself with them. Nor did He set up against them an opposing party. He did not represent or defend or champion any programme - whether political, economic, moral or religious, whether conservative or progressive. He was equally suspected and disliked by the representatives of all such programmes, although He did not particularly attack any of them. Why His existence was so unsettling on every side was that He did this simply because He enjoyed and displayed, in relation to all the orders positively or negatively contested around Him, a remarkable freedom which again we can only describe as royal. He had need of none of them in the sense of an absolute authority which was vitally necessary for Him, and which He could prescribe and defend as vitally necessary for others because it was an absolute authority.
On the other hand, He had no need consistently to beak any of them, to try to overthrow them altogether, to work for their replacement or amendment. He could live in these orders. He could seriously acknowledge in practice that the temple of God was in Jerusalem, and that the doctors of the Law were to be found in this temple, and that their disciples the scribes were scattered throughout the land, with the Pharisees as their most zealous rivals. He could also acknowledge that the Romans bore supreme rule even over the land and people of the divine covenant. He could grant that there were families, and rich and poor. He never said that these things ought not to be. He did not opposed other "systems" to these. He did not make common cause with the Essene reforming movement. He simply revealed the limit and frontier of all these things - the freedom of the kingdom of God. He simply existed in this freedom and summoned to it. He simply made use of this freedom to cut right across all these systems both in His own case and in that of His disciples, interpreting and accepting them in His own way and in His own sense, in the light shed upon them all from that frontier. It was just that He Himself was the light which was shed upon all these orders from that frontier. Inevitably their provisional and relative character, the ways in which they were humanly conditioned, their secret fallibility, were all occasionally disclosed - not in principle, only occasionally, but on these occasions quite unmistakeably - in His attitude toward them and His assessment of their significance.
But it was not these incidental disclosures of the freedom of God which made Him a revolutionary far more radical than any that came either before or after Him. It was the freedom itself, which could not even be classified from the standpoint of these orders. For where are these orders when He expresses both in word and deed that abasement of all that is high and exaltation of all that is low? Do they not all presuppose that the high is high and the low low? Was not the axe really laid at the root of all these trees in and by His existence?
In the last resort, it was again conformity with God Himself which constituted the secret of the character of Jesus on this side too. This is the relationship of God Himself to all the orders of life and value which, as long as there is history at all, enjoy a transitory validity in the history of every human place. This is how God gives them their times and spheres, but without being bound to any of them, without giving any of them His own divine authority, without allotting to any of them a binding validity for all men even beyond their own time and sphere, without granting that they are vitally necessary and absolutely authoritative even for their own time and sphere. In this way God Himself is their limit and frontier. An alien light is thus shed on them by God Himself as on that which He has limited. This is how He deals with them, not in principle, not in the execution of a programme, but for this reason in a way which is all the more revolutionary, as the One who breaks all bonds asunder, in new historical developments and situations each of which is for those who can see and hear - only a sign, but an unmistakable sign, of His freedom and kingdom and overruling of history. [Quoted from Karl Barth: Church Dogmatics, A Selection with Introduction by Helmut Gollwitzer, translated and edited by G. W. Bromiley (Edinburgh: T. & T. Clark, 1961), pp. 96-98.]
Almighty God, source of justice beyond human knowledge: We thank you for inspiring Karl Barth to resist tyranny and exalt your saving grace, without which we cannot apprehend your will. Teach us, like him, to live by faith, and even in chaotic and perilous times to perceive the light of your eternal glory, Jesus Christ our Redeemer; who lives and reigns with you and the Holy Spirit, ever one God, throughout all ages. Amen.