「📝」 doc(auth): should be complete

doc/auth/login.md

@@ -1,6 +1,65 @@
 # Login
 
 Abailable endpoints:
-- `/login`
-- `/login/google`
-- `/login/google/callback`
+- POST `/login`
+- GET `/login/google`
+- GET `/login/google/callback`
+
+Common return:
+- 500 with response 
+```json
+{
+    "error": "Internal server error"
+}
+```
+
+## POST `/login`
+
+Used to login
+
+Input needed :
+```json
+{
+    "user": "<string>",
+    "password": "<string>"
+}
+```
+
+Can return: 
+- 200 with response and cookie in header
+```json
+{
+    "msg": "Login successfully"
+}
+```
+- 400 with response
+```json
+{
+    "error": "<corresponding error>"
+}
+```
+
+## GET `/login/google`
+
+Used to redirect the user to the login page for google auth
+
+Always return:
+- redirect to the google auth url
+
+## GET `/login/google/callback`
+
+Used to get the callback from google and confirm the login
+
+Can return:
+- 400 with response
+```json
+{
+    "error": "<corresponding error>"
+}
+```
+- 200 with response and cookie in header
+```json
+{
+    "msg": "Login successfully"
+}
+```