Academy technologies are researched separately in each Grepolis city. This lets you specialize, but points spent in one polis do not automatically unlock the same technology elsewhere.
Choose the city role first
Decide whether the city will support land attack, defence, ships or expansion. Then inspect research costs and prerequisites and prioritize technologies that unlock units or improve actions you will use often.
Spend points deliberately
Research capacity depends on Academy development and may be affected by special buildings. Avoid copying a build from another world without checking your settings. Resetting research can have a culture cost, so plan ahead.
See the guides to land units, ships and the complete guide.