Android Studio 3.0.1 Error: Gradle project sync failed. Basic functionality (e.g. editing, debugging) will not work properly

This problem occurs when the Build Tools Version is not set for the project. You just set the build tools version by following this process...

By opening your project structure [File->Project Structure] and selecting the Build Tools Version from app's property tab in Modules section.

This will add build tools version to your gradle file (Module:app) and re-sync the project.

The problem caused by my connection. I needed to set proxy to download some components.

The error happens under fluctuating network. So at first make sure your connection is stable. Plus, if you are using any VPN check your gradle.properties is configured correctly.

The correct form of VPN connection on gradle.properties is as follows,

systemProp.http.proxyHost=127.0.0.1
systemProp.http.proxyPort=8080
systemProp.https.proxyHost=127.0.0.1
systemProp.https.proxyPort=8080

My host connection is 127.0.0.1, and its port is 8080 for both http and https.

Just one more thing, make sure adding https (It is mandatory).