Opens mailbox on yandex.ru with IMAP, reads the last message and all unread ones.

ReadYandexMailbox.java

import com.sun.mail.imap.IMAPMessage;
import java.util.Properties;
import javax.mail.Address;
import javax.mail.BodyPart;
import javax.mail.Flags;
import javax.mail.Folder;
import javax.mail.Message;
import javax.mail.Session;
import javax.mail.Store;
import javax.mail.internet.MimeMultipart;
import javax.mail.search.FlagTerm;

public void readYandexMailbox(String login, String password) throws MessagingException, IOException {
    Properties props = new Properties();
    props.setProperty("mail.store.protocol", "imaps");
    props.setProperty("mail.imaps.ssl.trust", "imap.yandex.ru");
    Session session = Session.getDefaultInstance(props, null);
    Store store;
    store = session.getStore();
    store.connect("imap.yandex.ru", 993, login, password);
    Folder inbox = store.getFolder("INBOX");
    inbox.open(Folder.READ_WRITE); // even though we only want to read, write persmission will allow us to set SEEN flag
    try {
        Message lastMessage = inbox.getMessage(inbox.getMessageCount());
        ((IMAPMessage)lastMessage).setPeek(true); // this is how you prevent automatic SEEN flag
        MimeMessage cmsg = new MimeMessage((MimeMessage)lastMessage); // this is how you deal with exception "Unable to load BODYSTRUCTURE"
        printMessage(cmsg);
        markMessageAsSeen(lastMessage, inbox);

        FlagTerm unreadFlag = new FlagTerm(new Flags(Flags.Flag.SEEN), false);
        Message unreadMessages[] = inbox.search(unreadFlag);
        for (Message unreadMessage : unreadMessages) {
            // SEEN flag here will be set automatically.
            printMessage(unreadMessage); 
        }
    } finally {
        inbox.close(true);
    }
}

private void printMessage(Message message) throws MessagingException, IOException {
    Address[] addresses = message.getFrom();
    for (Address address : addresses) {
        System.out.println("FROM: " + address.toString());
    }
    System.out.println("SUBJECT:" + message.getSubject());
    System.out.println("TEXT:" + getText(message).trim());
}

private void markMessageAsSeen(Message message, Folder folder) throws MessagingException {
    folder.setFlags(new Message[] {message}, new Flags(Flags.Flag.SEEN), true); 
}

private boolean textIsHtml = false; // if test is html, use html parser (e.g. org.jsoup)

// copy-paste from http://www.oracle.com/technetwork/java/javamail/faq/index.html#mainbody
private String getText(Part p) throws
            MessagingException, IOException {
    if (p.isMimeType("text/*")) {
        String s = (String)p.getContent();
        textIsHtml = p.isMimeType("text/html");
        return s;
    }
        if (p.isMimeType("multipart/alternative")) {
        // prefer html text over plain text
        Multipart mp = (Multipart)p.getContent();
        String text = null;
        for (int i = 0; i < mp.getCount(); i++) {
            Part bp = mp.getBodyPart(i);
            if (bp.isMimeType("text/plain")) {
                if (text == null)
                    text = getText(bp);
                continue;
            } else if (bp.isMimeType("text/html")) {
                String s = getText(bp);
                if (s != null)
                    return s;
            } else {
                return getText(bp);
            }
        }
        return text;
    } else if (p.isMimeType("multipart/*")) {
        Multipart mp = (Multipart)p.getContent();
        for (int i = 0; i < mp.getCount(); i++) {
            String s = getText(mp.getBodyPart(i));
            if (s != null)
                return s;
        }
    }
    return null;
}