Az Yashir: Hashem Shall Reign for All Eternity.
ה' ימלך לעלם ועד
Hashem shall reign for all eternity.
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HaRav Avigdor Miller zt”l (Praise, My Soul) explains that there are three aspects included in this one pasuk: a statement, a promise/acceptance, and a tefilah.
It is a statement of recognition that Hashem’s power, wisdom, and kindliness will continue unchanged forever. His love for the Avos and their descendants will continue forever. Each morning, we conclude the brachah before Shema with the words “הבוחר בעמו ישראל באהבה–Ha’bocheir b’amo Yisrael b’ahavah (Who chooses His people Yisrael with love).” “הבוחר–Ha’bocheir” is present tense. Hashem is choosing us, right now, with love. That will continue forever.
This pasuk is also a promise. In the tefilah of Maariv, we say “ומלכותו ברצון קבלו עליהם, משה ובני ישראל לך ענו שירה, בשמחה רבה, ואמרו כולם...ה' ימלך לעלם ועד – And His kingship they accepted willingly upon themselves, Moshe and B’nei Yisrael…” Because of their immense gratitude, they obligated themselves forever to do His will.
There is a difference between a “Ruler” and a King. A Ruler rules by force, whether the subjects accept the Ruler or not. A King, on the other hand, rules over his subjects through their acceptance. Hashem is our King because we accept His kingship willingly and happily. As for the rest of the world, Hashem is their Ruler.
This is what is meant later when we say “כי לה' המלוכה ומשל בגוים–Ki LaShem ha’m’luchah u’mosheil ba’goyim (For the sovereignty is Hashem’s and He rules over nations).”
For us, Hashem is King. For the nations, Hashem is their Ruler. We then conclude with “והיה ה' למלך על כל הארץ, ביום ההוא יהיה ה' אחד ושמו אחד–Then Hashem will be King over all the world; on that day Hashem will be One and His Name will be One.”
These concluding phrases stress the third component, a tefilah that Hashem should cause all men to forever recognize Him and accept Him as the sole King.
In the next segment, b’ezras Hashem, we will expand on “ושמו אחד–u’sh’mo echad.”