The Sanlun school, also known as the Three Treatise school, is a Chinese Madhyamaka school that emerged during the 6th century in China. It was founded by the Indian monk Kumarajiva and was later developed by his disciple Sengzhao. This school is based on the teachings of the Madhyamaka school of Buddhism, which emphasizes the concept of emptiness and the Middle Way.

The main teachings of the Sanlun school revolve around the concept of emptiness, also known as sunyata. This concept is derived from the Prajnaparamita sutras, which state that all phenomena lack inherent existence and are empty of self-nature. The Sanlun school believes that this emptiness is the ultimate truth and that all conventional truths are merely relative and dependent on causes and conditions.

The school also emphasizes the Middle Way, which is the path between extreme views of existence and non-existence. The Middle Way teaches that all phenomena are neither real nor unreal, but are dependent on causes and conditions. This concept is in line with the Madhyamaka school's idea of the two truths, the conventional truth and the ultimate truth.

Another important teaching of the Sanlun school is the concept of the Fourfold Negation. This concept states that all phenomena can be negated in four ways - as being neither existent, nor non-existent, nor both, nor neither. This helps to refute any extreme views and leads to a deeper understanding of emptiness.

The school also teaches the concept of dependent origination, which states that all phenomena arise and cease due to causes and conditions. This concept is closely related to emptiness and helps to explain the interdependent nature of all things.

In addition to these main teachings, the Sanlun school also places great emphasis on the study and interpretation of the Madhyamaka treatises, specifically the Madhyamakakarika, the Madhyamakavatara, and the Shunyatasaptati. These texts are considered the core teachings of the school and are studied and debated extensively by its followers.

Overall, the main teachings of the Sanlun school revolve around the concepts of emptiness, the Middle Way, the Fourfold Negation, and dependent origination. These teachings are aimed at helping individuals to develop a deeper understanding of reality and to overcome ignorance and attachment to the self.