This is a simple ImageDownloader which uses Picasso do download images and write them to a folder.

ImageDownloadManager.java

import android.content.Context;
import android.graphics.Bitmap;
import android.net.Uri;
import android.os.Handler;
import android.os.Looper;
import android.util.Log;

import com.squareup.picasso.MemoryPolicy;
import com.squareup.picasso.Picasso;
import com.squareup.picasso.RequestCreator;

import java.io.File;
import java.io.FileOutputStream;
import java.lang.ref.WeakReference;
import java.security.InvalidParameterException;
import java.util.HashMap;
import java.util.List;
import java.util.concurrent.LinkedBlockingQueue;
import java.util.concurrent.ThreadPoolExecutor;
import java.util.concurrent.TimeUnit;

/**
 * Helper to download Images. This takes set of Urls to download and a folder oath to cave the
 * files. Calls  onSuccess only if all images are downloaded. Else calls
 * onFailure()
 *
 * @author: bedprakash on 11/1/17.
 */

public class ImageDownloadManager {

  private static final String FORWARD_SLASH = "/";
  private static final String DOT = ".";

  public enum Task {
    DOWNLOAD, DELETE
  }

  public enum ImageSaveFailureReason {
    NETWORK, FILE
  }

  public interface Extensions {
    String PNG = "png";
    String JPEG = "jpeg";
    String WEBP = "webp";
  }

  public interface Callback {
    void onSuccess(ImageDownloadTask task);

    void onFailure(ImageSaveFailureReason reason);
  }

  private static final String LOG_TAG = ImageDownloadManager.class.getSimpleName();
  private static final Object LOCK = new Object();
  private static ImageDownloadManager sInstance;

  private Handler MAIN_HANDLER = new Handler(Looper.getMainLooper());
  private ThreadPoolExecutor threadPoolExecutor;
  private HashMap<ImageDownloadTask, Callback> callbacks = new HashMap<>();
  private Context context;

  private ImageDownloadManager(Context context) {

    if (sInstance != null) {
      throw new RuntimeException(
          "Use getInstance() method to get the single instance of this class.");
    }

    int NUMBER_OF_CORES = Runtime.getRuntime().availableProcessors();
    this.context = context.getApplicationContext();
    threadPoolExecutor = new ThreadPoolExecutor(
        NUMBER_OF_CORES * 2,
        NUMBER_OF_CORES * 2,
        60L,
        TimeUnit.SECONDS,
        new LinkedBlockingQueue<Runnable>());
  }

  public static ImageDownloadManager getInstance(Context context) {
    if (sInstance == null) {
      synchronized (LOCK) {
        if (sInstance == null) {
          sInstance = new ImageDownloadManager(context);
        }
      }
    }
    return sInstance;
  }

  public void addTask(ImageDownloadTask task) {
    if (callbacks.containsKey(task)) {
      Log.e(LOG_TAG, "Have another task to process with same Tag. Rejecting");
      return;
    }

    threadPoolExecutor.execute(new ImageDownloadRunnable(task));
    callbacks.put(task, task.callback.get());
  }

  private class ImageDownloadRunnable implements Runnable {

    ImageDownloadTask imageDownloadTask;

    ImageDownloadRunnable(ImageDownloadTask task) {
      this.imageDownloadTask = task;
      if (task == null) {
        throw new InvalidParameterException("Task is null");
      }
    }

    @Override
    public void run() {
      switch (imageDownloadTask.task) {
        case DELETE: {
          deleteFolder(new File(imageDownloadTask.folderPath));
          postSuccess(imageDownloadTask);
          break;
        }
        case DOWNLOAD: {
          downloadImages(imageDownloadTask);
          break;
        }
      }
    }

    private void downloadImages(final ImageDownloadTask task) {

      for (String url : task.urls) {
        Bitmap image = startDownload(url);
        if (null == image) {
          postFailure(imageDownloadTask, ImageSaveFailureReason.NETWORK);
          return;
        }
        if (!saveBitmapImage(image, imageDownloadTask.folderPath, url)) {
          postFailure(task, ImageSaveFailureReason.FILE);
          return;
        }
      }
      postSuccess(task);
    }

    @Override
    public boolean equals(Object o) {
      if (o instanceof ImageDownloadRunnable) {
        return imageDownloadTask.equals(((ImageDownloadRunnable) o).imageDownloadTask);
      }
      return super.equals(o);
    }
  }

  private void deleteFolder(File file) {
    try {
      if (file.isDirectory()) {

        // directory is empty, then delete it
        if (file.list().length == 0) {
          file.delete();

        } else {

          // list all the directory contents
          String files[] = file.list();

          for (String temp : files) {
            // construct the file structure
            File fileDelete = new File(file, temp);

            // recursive delete
            deleteFolder(fileDelete);
          }

          // check the directory again, if empty then delete it
          if (file.list().length == 0) {
            file.delete();
          }
        }

      } else {
        // if file, then delete it
        file.delete();
      }
    } catch (Exception e) {
      // e.printStackTrace();
    }
  }

  public static String getFileNameFromUrl(String url) {
    return url.substring(url.lastIndexOf("/"), url.length());
  }

  public static String getHashCodeBasedFileName(String url) {
    return url.hashCode() + DOT + getExtension(getFileNameFromUrl(url));
  }

  public static String getExtension(String fileName) {
    String extension = "";
    if (fileName == null || fileName.isEmpty()) {
      return extension;
    }

    int indexOfLastDot = fileName.lastIndexOf(DOT);
    if (indexOfLastDot != -1 && indexOfLastDot < fileName.length())

    {
      extension = fileName.substring(indexOfLastDot + 1);
    }

    return extension;
  }


  public static boolean saveBitmapImage(Bitmap bitmap, String path, String url) {
    File folder = new File(path);
    if (!folder.exists()) {
      if (!folder.mkdir()) {
        return false;
      }
    }
    try {
      String fileName = getHashCodeBasedFileName(url);
      String imagePath = path + FORWARD_SLASH + fileName;
      FileOutputStream fileOutputStream = new FileOutputStream(imagePath);
      bitmap.compress(getCompressFormatFromFileName(fileName), 100, fileOutputStream);
      fileOutputStream.close();
      return true;
    } catch (Exception e) {
      e.printStackTrace();
      return false;
    }
  }

  public static Bitmap.CompressFormat getCompressFormatFromFileName(String fileName) {
    switch (getExtension(fileName)) {
      case Extensions.WEBP:
        return Bitmap.CompressFormat.WEBP;
      case Extensions.JPEG:
        return Bitmap.CompressFormat.JPEG;
      default:
        return Bitmap.CompressFormat.PNG;
    }
  }

  private Bitmap startDownload(String url) {

    try {
      RequestCreator requestCreator = Picasso.with(context).load(Uri.parse(url));
      requestCreator.memoryPolicy(MemoryPolicy.NO_CACHE, MemoryPolicy.NO_STORE);
      return requestCreator.get();
    } catch (Exception e) {
      e.printStackTrace();
      return null;

    }
  }

  public static class ImageDownloadTask {
    private Object tag;
    public Task task;
    public List<String> urls;
    public String folderPath;
    public WeakReference<Callback> callback;

    public ImageDownloadTask(Object tag, Task task, List<String> urls, String folderPath,
                             Callback callback) {
      this.tag = tag;
      this.task = task;
      this.urls = urls;
      this.folderPath = folderPath;
      this.callback = new WeakReference<>(callback);
    }

    @Override
    public boolean equals(Object o) {
      if (o instanceof ImageDownloadTask) {
        return this.tag.equals(((ImageDownloadTask) o).tag);
      }
      return super.equals(o);
    }

    @Override
    public int hashCode() {
      return tag.hashCode();
    }

  }

  private void postSuccess(final ImageDownloadTask task) {
    final Callback callback = task.callback.get();
    if (callback != null) {
      MAIN_HANDLER.post(new Runnable() {
        @Override
        public void run() {
          callback.onSuccess(task);
        }
      });
    }
    callbacks.remove(task);
  }

  private void postFailure(ImageDownloadTask task, final ImageSaveFailureReason error) {
    final Callback callback = task.callback.get();
    if (callback != null) {
      MAIN_HANDLER.post(new Runnable() {
        @Override
        public void run() {
          callback.onFailure(error);
        }
      });
    }

    callbacks.remove(task);
  }
}