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 three free online books with different perspectives, refer to the chapters on Right View or the Four Noble Truths in each book:

What the Buddha Taught by Walpola Rahula available here - this is a fairly “rational” and western approach to the teachings
The Noble Eightfold Path by Bhikkhu Bodhi available here - this presents a somewhat more traditional approach to teachings
The Four Noble Truths by Ajahn Sumedho available here - this is a more intuitive approach to the four noble truths.

First Noble Truth

Suffering, stress, unease, these are the symptoms. Suffering is to be understood. (See the Buddha’s traditional first sermon on the Four Noble Truths)

  • Birth, aging, sickness, death, sorrow, lamentation, pain, grief, despair

  • Association with the unpleasant, separation from the pleasant

  • Not getting what one wants

  • “In brief” the Five Aggregates of Clinging are suffering. They are: form (rupa), feeling (vedana), perception (sanna), mental formations (sankhara), sense-consciousness (vinnana)

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

  • The Pain of Pain - dukkha-dukkha

    • 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 - vipariṇāma-dukkha

    • 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 vicissitude is included in dukkha as suffering produced by change (vipariṇāma-dukkha).

  • The Pain of Conditioned Existence - saṃkhāra-dukkha)

    • 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. In addition, conditioned things, including ourselves, are always changing because of events outside of our control. We have no ownership of them, so they are unpredictable and uncertain. We cannot make anything in the world behave as we wish, including our own bodies and minds.

  • Raṭṭhapāla’s summary of suffering https://suttacentral.net/mn82/en/sujato

    The world is unstable and swept away.
    The world has no shelter and no savior.
    The world has no owner—you must leave it all behind and pass on.
    The world is wanting, insatiable, the slave of craving.

Second Noble Truth

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

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

  • 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 specific way 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

  • 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, and breaking the cycle of being trapped in endless rebirths.

  • Nirvana cannot be defined. It is impossible to capture any real understanding of it in a bullet point like the one you are reading now.

  • 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 (see below) 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.