这里介绍两种方式，如下：

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一、逐次

private static final int PERMISSION_READ_EXTERNAL_STORAGE = 101;
private static final int PERMISSION_WRITE_EXTERNAL_STORAGE = 102;
private static final int PERMISSION_CAMERA = 103;
private void requestPermission() {
 if (ContextCompat.checkSelfPermission(this, Manifest.permission.WRITE_EXTERNAL_STORAGE)== PackageManager.PERMISSION_DENIED) {
  ActivityCompat.requestPermissions(this, new String[]{Manifest.permission.WRITE_EXTERNAL_STORAGE}, PERMISSION_WRITE_EXTERNAL_STORAGE);
 }
 if (ContextCompat.checkSelfPermission(this, Manifest.permission.READ_EXTERNAL_STORAGE) == PackageManager.PERMISSION_DENIED) {
  ActivityCompat.requestPermissions(this, new String[]{Manifest.permission.READ_EXTERNAL_STORAGE}, PERMISSION_READ_EXTERNAL_STORAGE);
 }
 if (ContextCompat.checkSelfPermission(this, Manifest.permission.CAMERA) == PackageManager.PERMISSION_DENIED) {
  ActivityCompat.requestPermissions(this, new String[]{Manifest.permission.CAMERA}, PERMISSION_CAMERA);
 }
}


@Override
public void onRequestPermissionsResult(int requestCode, String permissions[], int []grantResults) {
 switch (requestCode) {
  case PERMISSION_CAMERA: {
   if (grantResults.length > 0 && grantResults[0] == PackageManager.PERMISSION_GRANTED) {


   } else {
    Toast.makeText(this, "没有摄像头权限我什么都做不了哦!", Toast.LENGTH_LONG).show();
   }
   break;
  }
  case PERMISSION_READ_EXTERNAL_STORAGE: {
   if (grantResults.length > 0 && grantResults[0] == PackageManager.PERMISSION_GRANTED) {


   } else {
    Toast.makeText(this, "请打开存储读写权限，确保APP正常运行", Toast.LENGTH_LONG).show();;
   }
   break;
  }
  case PERMISSION_WRITE_EXTERNAL_STORAGE: {
   if (grantResults.length > 0 && grantResults[0] == PackageManager.PERMISSION_GRANTED) {


   } else {
    Toast.makeText(this, "请打开存储读写权限，确保APP正常运行", Toast.LENGTH_LONG).show();;
   }
   break;
  }
 }
}

网页题目：android6.0权限授权方法-创新互联
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