Some yeshivot see the ideal Jew as a "space cadet" in his idealistic dream-land, and yeshiva learning as a separation from the world. Contrarily, Rav Kook brings many proofs showing that the original Judaism, before being warped by exile, saw the ideal as practical pragmatism & the importance of learning Torah as united with "living the Torah". Being part of a Jewish society to fix all aspects of the world to implement a Living Torah & her ideals. He explains the halacha that one should pray where there are windows to show that our prayers, as the Torah, should be connected with the outside world. Even R. Shimon bar Yochai learned 12 years in the cave, 1st in order to analyze, & then to plan Jewish leadership to pragmatically fix society.
All of Torah is Important: Halacha, Aggada and Kabbala
Ein Aya, Shabbat 2, 249
One of the major innovations of Rav Kook and his yeshiva is not only to learn the Talmud but to learn the broader Torah, including Aggada and Kabbala, as well. In many yeshivas they skip or learn the stories and aggadata in the gemara very superficially, and in doing so, are unfortunately missing out on one of the most beautiful, appealing and attractive parts of Torah. Similarly Kabbala and Hassidut are becoming more and more popular, and Rav Kook, already 100 years ago, writes that this "broad Torah" is what will keep Judaism's appeal in the modern and post-modern world, and can even help "return" those who left the derech, who are searching for something deep, emotional and intellectual.
Rav Kook on How the Living Torah Must Be "Normal" & Not Contradict Life"
The Living Torah, or Torat Chaim, must not contradict normal life, & is not meant to aggravate nor make life difficult. Rav Kook teaches that God is described as "Melech Chafetz baChaim", and the physical world of work and even the secular aspects of life, should not be looked down upon. To the contrary, we should want to achieve and complete our plans in life, even in the field of hygiene and work. Especially in Eretz Yisrael, where the physical is also holy. Halacha, both Torah and rabbinic, is exact, and it's important to be meticulous, but not overly stringent, at the expense of life. Rav Kook provides a philosophic and hashkafic base for modern orthodoxy, and not shunning the secular world or secular studies.
Two Ways that Learning Torah Brings Us Closer to God:
In general there are 3 ways of coming close to God: most common, either through emotion or intellect, but then Judaism adds: or to be "similar" [=close] to Him. The greatest gift that He could give us is the "Tzelem Elohim", or capability of imitateo dei, being Godly. The she'ur discusses the advantages & disadvantages of each approach to Him. Most importantly, we can't understand His Essence, but we can amd should understand His actions. This is the ultimate in both the Rambam's rational and also the kabbalistic approach to Judaism. Rav Kook explains that the 13 traits of God, as well as the 10 sfirot, all detailus what to emulate. This has far-reaching ramifications for prayer, study as well as defining our goal and potential in life!