What are the principles of Buddhism?

There are totally 31 types of realms in a solar system. Infinite number of such world systems exist in the universe. Main items of the 31 types of realms can be shown as several kinds of heavenly realms, Human realm, Animal realm, Hungry ghost realm and Hell realms. Science can prove only two types from all of these realms; those are human realm and animal realm. There are an infinite number of living beings in the universe. Those living beings are endlessly rebirth in those realms.  This endless cycle of death and rebirth is known as Samsāra. Most often living beings are living in hell worlds as their home. They rarely come to the human realm or heavenly realms but again go to hell realms or to suffering realms. Rarely, a negligible number of them break the endless cycle of death - rebirth and reach to a permanent happy status known as Nirvana. At the moment of full enlightenment they perfectly realize Nirvana and it is irreversible. At the end of their last life they completely reach Nirvana.

Nirvana or ‘Spiritual Enlightenment’ is completely different from heaven or paradise as in some other religions. It is a mental status not a physical place.

Life on any one of the 31 realms has following characteristics:

1. Impermanent (This is known as Anicca).

2. Suffering compared to supreme happiness. (Suffering exists at birth, ageing, sickness, death,..etc.  This is known as Dukkha).

3. Non-self or Non-soul; only a combination of material and non-material sequences exists without a permanent part, but appears as a living being (known as Anattā).

These three characteristics are known as the ‘Three Marks of Existence’. Noble beings perfectly understand these characteristics. Existence in any world is suffering relative to supreme happiness. This is the First Noble Truth in summary. (The Truth of Suffering)

Always, living beings (including heavenly beings) live with their different kinds of cravings (avarice or Tanhā) , wrong views (delusions) and  defilements (Kleshas). So, they can't be aware of noble truths or the reality. Every kind of cravings causes a rebirth (explained in a later answer) and suffers. This is the Second Noble Truth in summary. (The Truth of the Origin of Suffering)

If anyone could understand these things (Noble Truths, Three Marks of Existence) perfectly and clearly just as we see something by our own eye, then he will be awakened from that instant with experiencing special kind of consciousness. This consciousness is called Magga-citta (we will discuss this in a later answer). Then, after the end of his current life he will reach to a permanent status of happiness known as Nirvana. He will not rebirth in any world again.

The only answer to the sufferings in the cycle of death and rebirth is enlightenment and reaching Nirvana. It is permanent without any sufferings. This is the Third Noble Truth in summary. (The Truth of the Cessation of Suffering)

There are only two types of self-awakenings known as Lord Buddha (Sammā-Sambuddha) and Solitary-Buddha (Pacceka-Sambuddha). They are very rare. (During the last hundred world cycles of our world system, only seven Lord Buddhas came into existence). All Lord Buddhas teach the same path to reach Nirvana. This path is known as the Noble Eightfold Path. By following this path, a being can attain Nirvana with a small effort compared to the self-awakening. Then he is called an Arhat. If anyone could attain Nirvana these days, it should be the result of following the noble eightfold path. (Lord Buddhas never recommended everyone to become a Lord Buddha. It is very suffering for a very long time in Samsara; Such a person has to do very difficult things for many lives. Such as donating his own blood more than the amount of water in the sea. Also, then there is a possibility of completely forgetting the goal. So, Mahayana Buddhism is different than the original Lord Buddha's teaching).

Noble eightfold path can be split into three steps known as "Threefold Training". Moral virtue (Sīla) is the first step to eternal happiness, Nirvana. Moral virtue is required to have a higher concentration of mind or tranquility of mind. This is called Samādhi.Samādhi is required to have a higher wisdom (Paññā). Higher wisdom is required to completely realize the reality (Four noble truths). This path is the Fourth Noble Truth in summary. (The Truth of the Way) 

Another important concept of Buddhism is “act and result”. This is known as Karma. We can make our lives less suffering (happy) in the cycle of rebirth by doing good deeds (positive-karmas). If someone does many good deeds, he will receive happy returns in the cycle of rebirth. On the other hand, if someone does many bad deeds (negative-karmas) there will definitely be bad returns. Karmas mainly become effective in next lives, that's why some people don’t believe it. Anyway, as the teachings of the Lord Buddha everything around us doesn’t happen according to past Karmas. There are five types of factors; Karma is only one of these factors. (We will discuss in a later answer.)

Actions or thinking done with greed, anger or ignorance mind (also can be combinations of these) are bad Karmas, which will result bad things in the future. Karmic formation is a mental (related to mind) thing. But, Karmas are generated for your actions since actions done by the mind. For example; when you give a donation, your many thoughts arise without greed or anger in mind. So, it is a good Karma which will result many good things in the future. Karma will mainly depend on your mind. If two people donate exactly the same thing, the strength of the resultant Karma will be different, since they will not have exactly the same kind of mind when donating. Noble beings don’t have any greed, anger or ignorance. Their mind is perfectly detached from greed, anger or ignorance about life. So, there is no good or bad Karma generated for their thinking or actions.