The Four Noble Truths can be understood both intuitively and intellectually. You may find one way or the other works better for you, but ideally you can understand them both ways, using both sides of your mind to fully comprehend them. Here are two free online books with different perspectives:

What the Buddha Taught by Walpola Rahula available here - this is a fairly “rational” and western approach to the teachings. He covers the Four Noble Truths in the first few chapters.
The Four Noble Truths by Ajahn Sumedho available here - this is a more intuitive approach to the four noble truths.

Bhikkhu Bodhi wrote chapter 3 of The Buddha and His Teachings. He has a more traditional teaching style. His chapter was adapted from his book The Noble Eightfold Path which is freely available here if you would like to read further.

First Noble Truth

First Noble Truth - Suffering, stress, unease, these are the symptoms that cause us to seek answers and solutions for our lives. The Pali/Sanskrit word for this is Dukkha/Duhkha. Suffering is to be understood. (See the Buddha’s traditional first sermon on the Four Noble Truths)

  • Living brings us into contact with many types of dukkha such as birth, aging, sickness, death, sorrow, lamentation, pain, grief, and despair.

  • It is caused by association with the unpleasant and separation from the pleasant.

  • It is caused by not getting what we want.

  • It is caused by the Five Aggregates of Clinging. The aggregates are how Buddhists explain our sense of “me” caused by our body and mind. The aggregates are: our bodily form (rupa), feeling (vedana), perception (sanna), mental formations (sankhara), and sense-consciousness (vinnana).

  • The three traditional types of dukkha are ordinary pain, the pain of change, and conditioned existence:

  • The Pain of Pain

    • All kinds of suffering in life like birth, old age, sickness, death, association with unpleasant persons and conditions, separation from loved ones and pleasant conditions, not getting what one desires, grief, lamentation, distress – all such forms of physical and mental suffering, which are universally accepted as suffering or pain, are included in dukkha as ordinary suffering (dukkha-dukkha).

  • The Pain of Change

    • A happy feeling, a happy condition in life, is not permanent, not everlasting. It changes sooner or later. When it changes, it produces pain, suffering, unhappiness. This is included in dukkha as suffering produced by change (viparinama-dukkha).

  • The Pain of Conditioned Existence

    • This type of pain is the most subtle of the three. Because all objects and events are a result of past causes, nothing in this world can be said to have its own essential nature. It is “empty” of a true nature, its creation and present condition arose from conditions in the world around it. We ourselves are also conditioned, we are always being changed by events outside of our control. We have no ownership of them, so the changes we experience are unpredictable. We cannot make anything in the world behave as we wish, including our own bodies and minds, everything is conditioned by other things (sankhara-dukkha).

Second Noble Truth

Craving and aversion, both arising from ignorance, are the cause of suffering. Craving is to be abandoned.

  • Our ignorance causes selfish desire and greed (tahna), and it causes aversion in the form of fear, hatred, contempt, and indifference to the suffering of others. The Pali word tanha is related to the idea of thirst or greed.

  • We often suffer because of our fears, desires, and expectations.  When we want something (or someone) that we believe will make us happy, we are unhappy while we don’t have it.  Once we get it, we worry that we will lose it.

  • Because of our ignorance we seek out unreliable things in the world that we think will satisfy our craving. It could be a person, group, thing, place, job, situation, idea, or way of life. We also seek to escape from painful and unpleasant situations.

  • When we feel pain, we then feel aversion to our pain which can make us suffer even more than the original pain did. We then crave pleasure to escape from all this suffering, causing more problems (Dart Sutta).

  • The traditional explanation of how craving arises and causes problems are outlined in the chain of dependent origination.

  • The teachings explain craving in several different ways to help us recognize and understand it, such as the Three Types of Craving, Four Types of Clinging, Three Poisons, Four Nutriments, and the Eight Worldly Winds.

  • A basic part of the ignorance that causes our craving is our misunderstanding of the self, our self view. We are always trying to build up and defend the self and defend the things we identify with such as our family, possessions, nation, culture, religion, etc.

  • Wholesome desire that doesn’t involve clinging or selfishness is sometimes called dhamma-chanda. Examples of dhamma-chanda would be an aspiration to follow the path and a commitment to develop Right Intention.

Third Noble Truth

The cessation of suffering, the end of clinging - Nirvana/Nibbana. Cessation is to be realized.

  • Nirvana means to be free of clinging, craving, and suffering in this very life. From a metaphysical point of view it is breaking the cycle of being trapped in endless rebirths.

  • Ajahn Chah defined Nirvana as simply “The reality of non-grasping”.

  • Nirvana cannot truly be defined with words, it is something that must be experienced.

  • Nirvana is not an “all or nothing” experience. It is possible to get a taste of nirvana in everyday life as we learn to stop clinging so tightly to unreliable things.

  • How does one approach Nirvana? A traditional way to think of progress on the Buddhist path is through breaking the 10 Fetters:

    • Belief in a permanent, unchanging self, the idea that the aggregates are “you”. (sakkāya-diṭṭhi)

    • Doubt or uncertainty, especially about the Buddha's teachings (vicikicchā)

    • Believing that mechanically performing some method or technique or trick can save you. It’s the idea that you can solve your problems with shortcuts and life hacks to avoid the real work of understanding yourself. (sīlabbata-parāmāsa)

    • Sensual desire

    • Ill will

    • Desire for material existence, rebirth

    • Desire for immaterial existence

    • Conceit - a subtle sense of self

    • Restlessness

    • Ignorance (avijjā)

  • The eightfold path gives you the discipline and insight to break the first 3 fetters to reach stream entry and see the truth of the path. Breaking the remaining 7 leads to higher and higher states till one breaks the final fetter and becomes enlightened, an Arahant or Noble One.

Fourth Noble Truth

The way leading to cessation, which is the Eightfold Path. The path is to be followed. It is to be cultivated within oneself. It begins and ends with Right Understanding.

The Eightfold Path

  1. Right View - Understanding karma and the four noble truths.

  2. Right Resolve (sometimes called right thought or right aspiration) - the resolve to renounce violence, to renounce hatred and practice goodwill instead, and to renounce one’s attachment to worldly things that impede progress on the path.

  3. Right Speech - no lying, no abusive speech, no divisive speech, no idle chatter.

  4. Right Conduct or Action - no killing or injuring, no taking what is not given, no sexual misconduct.

  5. Right Livelihood - no trading in weapons, living beings, meat, liquor, or poisons.

  6. Right Effort - preventing the arising of unwholesome states, and generating wholesome states (the Seven Factors of Awakening).

  7. Right Mindfulness (sati) - Watching over the mind and developing insight into the true nature of things.

  8. Right Samadhi (concentration) - Calming and gathering the mind to develop one’s peace, joy, clarity, and equanimity.