Trace out the grown of Buddhism? …

a) The Growth of Buddhism

i.Buddhism grew rapidly both during the lifetime of the Buddha and after his death. 
ii.It appealed to many people dissatisfied with existing religious practices and confused by the rapid social changes taking place around them.
iii.The importance attached to conduct and values rather than claims of superiority based on birth, the emphasis placed on metta(fellow feeling) and karuna(compassion), especially for those who were younger and weaker than oneself, were ideas that drew men and women to Buddhist teachings.
iv.Buddhism grew due to Buddhist text-Tipitaka (the VinayaPitaka, SuttaPitaka, AbhidhammaPitaka), the Dipavamsa&Mahavamsa, Ashokavadana, Jatakas and Buddhist hagiography.
v.Buddhist Sanghas, Bhikkhus and Bhikkhunis spread the message.
vi.Stupas
vii.Ashokan pillars and inscriptions
viii.Dhamma–mahamattas
ix.Buddhist sects –Hinayana and Mahayana
x.Support of Rulers
xi.Foreign pilgrims

b)  

Upon the death of Gautama Buddha in 400 BC, Buddhism divided into two sects: Mahayana and Hinayana

The Mahayana sect, which means ‘Great Vehicle’ in Sanskrit, believed in the divinity of the Buddha. The sect encouraged idol worship in Buddhism

The Hinayana sect, meaning ‘Small Vehicle’ in Sanskrit, did not believe in the divinity of the Buddha. It stressed on individual salvation through self-discipline and mediation.