In Sanskrit, the word swastika is a combination of 'su' (meaning 'good') and 'asti' (meaning 'to exist') — often getting translated as 'all is well.' The swastika is thus understood to be a symbol of auspiciousness and good fortune.

Though the Nazi symbol was originally called the hakenkreuz (meaning 'hooked cross)', early translations of Adolf Hilter's "Mein Kampf" into English substituted swastika for hakenkreuz, thereby popularizing the notion of a "Nazi swastika".

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The swastika is regularly painted or written on Hindu homes, businesses, printed materials, cars, temples, and ashrams. Many Hindus adorn the threshold of the front entrance to their homes with the swastika. Especially during Diwali, Hindus may wash away old swastikas and reapply them, or include them as part of their rangoli (a traditional art form using dyed powders, rice and grains, or flowers to decorate the ground of courtyards). Often during Diwali, the swastika is created by artfully arranging diyas (clay lamps).

Though many Hindus displaying the swastika are doing so in the spirit of using it as auspicious and attractive decoration, the four limbs of the swastika are also interpreted with deeper symbolic meaning.

The four limbs can be interpreted as representing:

• The four Vedas (foundational scriptures of Hinduism), the Rig Veda, the Yajur Veda, the Sama Veda, and the Atharva Veda.
• The four traditional stages of life: Brahmacharya (youth/student), Grihasta (adult/family), Vanaprastha (elder); Sannyasa (old age/renunciation of the world).
• The four goals of life: Dharma (right conduct), Artha (prosperity), Kama (pleasure), Moksha (spiritual liberation).
• The four yugas (cyclical world ages): Satya Yuga, Treta Yuga, Dvapara Yuga, Kali Yuga. We are currently in the shortest yuga, and the last before the cycle begins again, the Kali Yuga.
• The four seasons: Though not everyplace on Earth experiences the seasons in the same way and some places translate the procession of the year's natural phenomena in different terms, the four limbs of the swastika can also be taken to represent winter, spring, summer, fall. The procession of the seasons mirroring the procession of the stages of life.
• The four cardinal directions.

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Yes. In 2008, the second Hindu-Jewish leadership summit took place in Jerusalem. The summit issued the follow declaration, recognizing the importance and positive intent of Hindus using the swastika:

"Swastika is an ancient and greatly auspicious symbol of the Hindu tradition. It is inscribed on Hindu temples, ritual altars, entrances, and even account books. A distorted version of this sacred symbol was misappropriated by the Third Reich in Germany, and abused as an emblem under which heinous crimes were perpetrated against humanity, particularly the Jewish people. The participants recognize that this symbol is, and has been sacred to Hindus for millennia, long before its misappropriation."