Assalaamu alaykum wa rahmatullaahi wa barakaatuhu. Some books mention hadiths but do not cite its source (Bukhari, Muslim, etc.), nor do they mention the authenticity of the hadith. So what should I do? Should I ignore the hadith, believe in it, or disbelieve in it? Or should I not read the book?

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

You should search for the classification of the hadeeth in the reliable Hadeeth books or ask specialized scholars about it. Searching has become easier nowadays through the electronic search engines and the ease of communicating with scholars.

Allah knows best.