There are many dimensions of Teilhard’s vision of evolution.  Some of them can be seen in things he wrote, and in the writings of others, presented here.

The key to understanding Pierre Teilhard de Chardin is understanding how important evolution is to his worldview.  He wrote, “Evolution is a general condition to which all other theories, all hypotheses, all systems must bow and which they must satisfy henceforward if they are to be thinkable and true. Evolution is a light illuminating all facts, a curve that all lines must follow.”

From early childhood Teilhard searched for something that was not perishable.  Something that was constant, everlasting.  Ironically, he found that constancy, in constant change.  In the fact of evolution on a cosmic scale. 

“At first, I was far from understanding and appreciating the importance of the change I was undergoing. All that I can remember of those days (apart from that magic word ‘evolution, which haunted my thoughts like a tune.) All that I can remember is the extraordinary solidity and intensity I found in the English countryside, particularly at sunset, when the Sussex woods were charged with all that ‘fossil’ Life, which I was then hunting for.”  

His particular understanding of evolution rests on his insight that all matter is infused with spirit, or consciousness, and that the arc of evolution can be seen as the evolution of consciousness. 

I believe that the universe is an evolution.
I believe that evolution proceeds towards spirit.
I believe that spirit 1 is fully realized in a form of personality.
I believe that the supremely personal is the universal Christ.

Like every other form of human knowledge, religious psychology is built upon experience. It needs facts. And since the circumstances are such that the facts occur only at the deepest level of men’s consciousness, this branch of knowledge cannot develop until individuals supply the necessary ‘confessions’.

It is entirely with this sort of documentary purpose in mind that I have tried to pin down, in what follows, the reasons for my faith as a Christian, with the shades of emphasis it bears, and also its limitations or difficulties. I in no way believe that I am better or more important than any other man: it simply happens that for a number of accidental reasons my own case is significant, and on that ground it is worth recording.
~ Introduction to “How I Believe” in Christianity and Evolution, Teilhard de Chardin, pp. 96-132

Teilhard’s grand opus is The Human Phenomenon, previously translated as The Phenomenon of Man.  He started writing it in 1938, when he was 57 years old, and tried ceaselessly, but without success, to get Jesuit permission to publish it. It was published posthumously after his death in 1955. 

~ The Human Phenomenon, Pierre Teilhard de Chardin, transl by Sarah Appleton-Weber, 1999, Harper Collins Publishsers, Inc.

The Human Phenomenon details in scientific terms the emergence of everything through the process of cosmogenesis, or evolution.  In it he establishes principles such as the law of complexity-consciousness. 

“One of Teilhard’s great discoveries related to the theory of evolution is his Law of Complexity=Consciousness. Simply put, this law reflects the tendency in matter to become more complex over time and at the same time to become more conscious. Teilhard recognized that this tendency in material things toward higher levels of complexity leading to higher levels of consciousness is a pattern that seems to guide the evolution of the entire universe.” 
~ Louis M. Savary, Teilhard Studies Number 68, Spring 2014, “Expanding Teilhard’s ‘Complexity-Consciousness’ Law”  (American Teilhard Association)

Pope Pius XII, in his 1950 Encyclical “Humani Generis” (“Of the Human Race”) was the first pope to make an official statement on evolution: 
“The Teaching Authority of the Church does not forbid that, in conformity with the present state of human sciences and sacred theology, research and discussions, on the part of men experiences in both fields, take place with regard to the doctrine of evolution, in as far as it inquires into the origin of the human body as coming from pre-existent and living matter—for the Catholic faith obliges us to hold that souls are immediately created by God.”

Pope John Paul II, in a letter to the head of the Vatican Observatory, wrote:
“Today, almost half a century after publication of the encyclical, new knowledge has led to the recognition of the theory of evolution as more than a hypothesis.  It is indeed remarkable that this theory has been progressively accepted by researchers, following a series of discoveries in various fields of knowledge.  The convergence, neither sought nor fabricated, of the results of work that was conducted independently is in itself a significant argument in favor of the theory.”

~ The Vatican’s View of Evolution: The Story of Two Popes,”  by Doug Linder (2004)
Written by a law professor, this article provides a detailed summary of the popes and evolution.

“Pierre Teilhard de Chardin: a visionary in controversy,” by Clément Vidal is an examination of Teilhard’s vision of evolution from the perspective of a scientist, published by the National Institutes of Health, 2021.

”This broad evolutionary vision made Teilhard see cosmic evolution in a single sweep, from energy, matter and particles, to chemistry, life, culture and technology. This standard master narrative at the foundation of all sciences is so natural today that it’s hard to appreciate that Teilhard was one of the very first thinkers to fully embrace and argue for the unity of cosmic evolution.”

As a palaeontologist, Pierre Teilhard de Chardin (1881–1955) was comfortable embracing large evolutionary time scales. This is natural for the science of palaeontology, but Teilhard went further in his attempt to foresee the future across a similar evolutionary sweep. Teilhard introduced a new -and often controversial – cosmological vision where evolution is not random, but has a direction towards increasing complexity and consciousness. Centrally, he argued that the next evolutionary stage would be of a planetary nature, a sphere of thinking emerging out of the biosphere that he called the noosphere.