In the book that I read recently (Mantram Handbook by Eknath Easwaran), he advises that one should repeat the mantram silently, whenever the mind is free, in day to day instances also, like waiting in a queue, etc. Overall, the sense of his conception of mantra seems to be limited to repeating some word along with an associated idea. This seems like some elementary meditation practice of keeping the mind fixed and not letting it wander, something like the popular, Buddhist Mindfulness meditation. Most of his quotations are either Gandhi, or Christians like some Brother Lawrence, Teresa, Meister Ekhart but also refer to a few sayings of Sri Ramakrishna, that too for namesake. Given that this is the case, I don't know how reliable his literature is on this subject. (His commentary on Upanishads-Essence of the Upanishads seemed pretty good)
However, as far as I have heard, mantra has an associated sound/vibration component too. Its not just repeating of words and ideas. Also, repeating mantras is said to be part of the integrated Raja Yoga/Mantra Yoga systems, and I don't think it is effective if one simply picks and chooses components that suit their religious sensibilities. It is regarded as being dangerous too. For example, Swami Vivekananda, in one of his lectures (I think raja-yoga), has said that Mohammad, the founder of the Islamic religion was a misguided person, because he didn't properly understand what he was doing(raja yoga according to Swamiji) and it led him to founding such a violent creed that preaches intolerance of any criticism.
Edit 1: Recently, I found this link, which advocates chanting Krishna's name while working, standing, etc. everywhere. The transcript is a bit long to read, here's the relevant part in short:
Śyāmasundara: You were saying earlier that we can also supplement our Kṛṣṇa consciousness while we're working, hammering the nails.
Śyāmasundara: So chanting along with devotional service, performing our duties while concentrating on Kṛṣṇa, is also part of the process, isn't it?
Prabhupāda: Yes. Anything, any way. The whole idea is manāḥ kṛṣṇe niveṣayet (SB 7.1.32). Mind should be fixed up in Kṛṣṇa. That is the process. Either you go through philosophy or through arguments or through chanting. Any way. That is recommended in the Bhagavad-gītā. Yoginām api sarveṣāṁ (BG 6.47). Of all kinds of yogīs. In the . . . you might have read it. Yoginām api sarveṣāṁ. I think Maharshi has translated this Bhagavad-gītā? And in the Sixth Chapter . . .? You have read it?
Easwaran, in his book, says that the rhythm in which it is repeated does not matter, whether it is repeated fast or slow does not matter. Again, I find this odd, as I have seen people associated with the tradition observing various rules while chanting mantras aloud. Also, I happened to glance over some of the pages of Mantra Yoga by Swami Sivananda Saraswati. I don't think Easwaran's views are supported there either. In this context, my question can be divided into the following sub-parts:
- What are the various uses of mantras? By this I also mean, Can they be used for non-visual meditation too? What do the various Hindu spiritual leaders, acharyas, saints and the scriptures say on these various uses?
- What are some good resources/books to learn about mantras on your own for Hindus. I mention Hindus, because other religions/atheists tend to purposefully skip the contents which stand at odds with their ideologies. I don't have any such restrictions, hence I would like to explore the subject in its entirety. Also, is the mantram practice suitable for someone, who hasn't had a proper initiation by a guru/sanyasin? (I had my upanayana ceremony when I reached of age, but I was too young and rebel minded then and grumpily accepted whatever I was told to do. I considered myself as an atheist at that point of time, due to media/pop culture conditioning. I don't think that counts as initiation.) If so, why? What purpose does initiation serve? Is it only about giving the mantra or also sustained support of an understanding, mature person throughout the spiritual proccess?
- Is initiation by a guru absolutely necessary for all mantras? What is the position of this proposition for different mantras, like generic popular mantras used by the Hare Krishna ISKON movement like hare krishna mantra, repeating the name rama-rama , mantras popularly used in almost every hindu household like Om namah Shivay, mantras said to have powerful psychological effects like mantras from the Durga Saptashati (hymns to the goddess).
On reading some links on the answers provided below, I understand that the answerers say that mantras cannot be repeated without initiation, quoting the scriptures directly. However, My question is not limited to the shastras. I would like to understand the position of this statement expressed by the new Hindu gurus also. By new Hindu gurus, I mean people who wrote/practiced Hinduism and preached about it. They might have taken a liberal interpretation of the sastras, not literal meanings in Sanskrit, and they are widely considered Hindu by the large, practicing Hindu community in India and elsewhere and are much held in much esteem by the community. Some examples are Swami Vivekananda, Sri Aurobindo, Sri Ramakrishna, Swami Sivananda Saraswati, Yogananda Paramhansa, Srila Prabhupada, Eknath Easwaran, Sadhguru.
Anyways, the sastras were supposed to be updated with time by men well read in sastras and possessing valid experiences (on the basis of adhikara), and they couldn't be updated traditionally, because the institutions, mathas, and temples were destroyed by invaders and thanks to the secular government, they don't function anymore/ lie defunct. So, in my opinion, maybe, the initiation part and some of the rituals might be outdated. For example, I think Chaitanya Mahaprabhu at the time of Islamic invasions, made some changes too to adjust according to changing times.
As for other uses of mantra, I read in Sundara - Yogic Therapy (primarily a book on hatha yoga), that mantras can be used for pranic therapy and divine healing. He was primarily a hatha yoga guru, but was initiated into vedanta too by a advaita vedantin, so he is also part of the continuous guru-shishya parampara.
Edit2:I remembered another innovative use that I saw a while ago. This video shows British kids reciting Sanskrit shlokas from the Upanishads to improve their pronounciation. Though not technically a mantras, positive thoughts in the Sanskrit language are associated with mantras.I am sure there are other uses as well.
On the last part, about sources, I am not looking for a collection of mantras as such, like the tantras. I wish to read a book, explaining the uses of mantras, the procedure to be followed while reciting a mantra, the various precautions to be taken, about health benefits, too, if any such exist. Please note that when I am asking for such resources, it is not simply for fun/research. I intend to practice. For examples of some such books, Mantra Yoga by Swami Sivananda Saraswati, Mantra Yoga and Primal sound by David Frawley, Meditation and Mantras by Swami Vishnu Devananda.
Another note: They need not be purely Hindu in nature. For example, Vajrayana Buddhism shares many features with Hinduism/Tantra, hence a suitable book can be mentioned too. For Example).
I found these books while surfing internet and goodreads book recommendations. I am sure experts here can lead me to better sources/ verify these are good sources. Please note: I am looking for English sources. Though I am literate in Hindi, I am not comfortable in the language, as I have a habit of reading books in English. Please post Hindi books only if no English alternatives are available/ the Hindi books are much better in quality/calibre than the English ones.