How to Install Sdk in Android Studio in Windows 10
The Android software development kit (SDK) includes different components, including SDK Tools, Build Tools, and Platform Tools.  The SDK Tools primarily includes the stock Android emulator, hierarchy viewer, SDK manager, and ProGuard.  The Build Tools primarily include          aapt          (Android packaging tool to create          .APK),          dx          (Android tool that converts .java files to          .dex          files).  Platform Tools include the Android debug shell, sqlite3 and Systrace.
The Android SDK can be installed automatically using the latest version of Gradle or downloading the Android SDK manually in several different ways. Below is an overview of all different approaches.
Installing the Android SDK (Automated Way)
Gradle 2.2.0 now supports downloading automatically dependencies. Make sure to upgrade to the latest Gradle version. The Gradle plugin to manage dependencies is now deprecated.
Installing for Ubuntu Linux
If you are using Ubuntu 15.04 or 15.10, make sure to install the following packages.  Otherwise, you may notice          No such file or directory          when running trying to execute the          aapt          program that is part of the Android SDK toolset:
          sudo apt-get install libc6-dev-i386 lib32z1 openjdk-8-jdk                Installing the Android SDK (via Homebrew)
Assuming you have macOS/OS X running, you can use Homebrew to install the Android SDK.
- Install Homebrew - the package manager for macOS/OS X
 - Run the following commands:            
brew tap homebrew/cask brew install --cask android-sdk 
This will install the Android SDK tools in          /usr/local/Cellar/android-sdk/<version number>        
Installing the Android SDK (Manual Way)
You will need to download the Android SDK without Android Studio bundled. Go to Android SDK and navigate to the SDK Tools Only section. Copy the URL for the download that's appropriate for your build machine OS.
          
        
Use          wget          with the correct SDK URL:
          $ wget https://dl.google.com/android/repository/tools_r25.2.3-macosx.zip                          Unzip and place the contents within your home directory. The directory names can be anything you like, but save the files in somewhere easy to find (i.e. ~/android-sdk).
Run the          sdkmanager          tool:
          $ tools/bin/sdkmanager --update $ tools/bin/sdkmanager "platforms;android-25" "build-tools;25.0.2" "extras;google;m2repository" "extras;android;m2repository" $ tools/bin/sdkmanager --licenses                                    
        
Now it's time to set your build environment's          PATH          variable and other variables that will be use to locate Android.
Edit your          .bash_profile          file. If you're not using bash, edit the right config file for your environment.
                      # Android                        export                        ANDROID_SDK_ROOT            =/Users/ciandroid/android-sdk-macosx            export                        PATH            =            $PATH:$ANDROID_SDK_ROOT/tools                Save and quit. Reload          .bash_profile:
                      $                        source            ~/.bash_profile                Installing via the GUI
At the prompt, type          android          and hit Enter to launch the Android SDK Manager in a window. If this doesn't work, your          PATH          variable has not been set up with the Android SDK location.        
          
        
You will want to install the same Android SDK packages on your build machine as you did to get Gradle running locally. Before you begin, take a look at the          build.gradle          file in your project.
Packages to install
Here are the SDK package names you'll definitely wish to select:
-             
Tools > Android SDK Tools -             
Tools > Android SDK Platform-tools -             
Tools > Android SDK Build-tools - One version of the Android Platform.  E.g.,            
Android 5.1.1 (API 22). It should be the one you named in theandroid: compileSdkVersionsection of yourbuild.gradlefile. 
You will also want to download the extras:
- Android Support Repository
 - Android Support Library
 
Note: Choose the Android SDK Build-tools for the version of Android that you listed in the          build.gradle          file as the          android: buildToolsVersion          target. If your          build.gradle          says        
                      android            {            buildToolsVersion            '21'            ...            }                          then make sure to download that API version in the Android SDK Manager.
Installing via the Command Line
You can also download the SDK packages using the command line with the          --no-ui          parameter.
          android update sdk --no-ui --all                If you want to be selective about installing, you can use          android list          to view all the packages and apply the          --filter          option for selective installs:
          sudo android update sdk --no-ui --filter platform-tools,tools                If you decide to be selective about which packages to be installed, make sure to include the extra Android Maven repository. Otherwise, you may not be able to use the latest support design library.
          android update sdk --no-ui --all --filter extra-android-m2repository                          There is currently no filter to install the build tools directly. See this ticket for more information.
How to Install Sdk in Android Studio in Windows 10
Source: https://guides.codepath.com/android/installing-android-sdk-tools