No, there is only Poder

You could change the tense: Can I ... = Puedo ... May I ... = Podría ...

I would also like to know if this is the common way to say, "May I..." From the dropdown menu when you hover over "Puedo" in this sentence, it looks like "May" is a good translation here.

I guess if someone next to you is reading a magazine and something caught your eye you could ask them "Can I see the magazine for a second?"

The translation is see, but it's assumed you're going to probably read it. It's like if your reading the newspaper and some asks to see it, instead of saying can I read that? There's a bit of a connotation that it will be a quick look. Puedo Leer LA revista ? Ignoring the unnecessary caps that my phone added haha, would technically be can I read the magazine. Rather than think the person is asking if they have the ability to read the magazine, or if they have permission to read it (both could be accurate if the context was a child asking) the normal translation is can I read it and it's interchangeable with ver since the assumption is that your not going to just look at it, but read it.

I like your point. It is a good point!

For example (in a dialog):

María: "Qué hiciste anoche?" ... ...(What did you do last night?)

Olga: "Vi TV." .... ...(I watched TV.)

Note: To say that Olga "saw" TV is too literal, in going from Spanish to English.

By the same token, "ver" a magazine sounds better as "to look at" (we wouldn't use "mirar" in either of the two cases, either).

CAVEAT: "Poder" expresses an ability to do something.

Puedo trepar árboles. (I can climb trees.)

Puedo trepar árboles? (Can I climb trees?)...Only YOU know if you "can" do it, or not!)

"MAY I look at the magazine?" always & traditionally involves the polite asking of permission to do so:

"Me permites ver la revista?"

Note that it is my observation that things change in the way ideas are expressed, based on the interaction of two languages across a border from each other. Case in point:

*"Que tengas un buen día!"*

This is gramatically incorrect. My South American friends would still be surprised at such a sentence; whereas, my Mexican friends who live across the border from the U.S. accept this wording, already.

The proper sentence is "Que pases un buen día." (To "pass the time" or even "to spend the time"... but never "to have" [possess] a good day). Tener shows possession, only.

Know what I mean?

To recap, the same applies to --PODER--. One does not ask if one "can do something". (The person already knows if they have the ability [i.e., capability] to do something, or not.) And, one would certainly not ask another if they were able to do it. Now, if they were seeking permission to do something (i.e., ver la revista), then the verb for "permit/allow" (-permitir-) is still the right way of saying it: notwithstanding the odd changes that are occurring in the (Spanish) language because of those interactions that I've already noted, above.

Postscript:

I don't like referencing my age, but I will do it, here, anyway. Over 60 years ago, when one of the neighbor kids came over, to play, he would often ask, "Can I watch TV?" The adult, in the room, always corrected his English by saying "MAY I watch TV?"

Even back then, here in the U.S., improper English was creeping into the language. We always asked permission to do something by asking "May I...?" (and never with the words "Can I...?").

So, it looks like English began to accept improper grammar (usage) a long time ago: and, I just hope Spanish doesn't begin to do the same...

...right down that same rabbit hole!

No. You don't conjugate the second verb. We don't do it in English either ("can he reads the magazine?").

I would like to know this as well. I am not seeing anyone comment on these types of questions which are more important questions than knowing whether it's reading or seeing.

I have only ever encountered revista as magazine, but maybe duolingo has used a vernacular; stick with revista and you'll be fine. Furthermore, maybe thinking of it as the|a review will help commit it to memory.

You will see the re prefix throughout Spanish, sometimes it makes sense and other times less so.

Examples: http://info.openanswers.org/the_spanish_verb_prefix_re

la vista means 'the view' - revista is the word for magazine

If the pronoun 'yo' is used, the statement would be 'yo puedo ver la revista'. If this is going to be a question, the wording is 'puedo yo ver la revista ? '. If 'yo' is not used, a sentence is distinguished by a statement by use of question marks if written, and by voice inflection if spoken.

Since I'm not sure which version of the exercise you saw (several feed into the same comment at times), I can only answer from the POV of English grammar. "I can" (subject verb) signals a sentence, while "can I" (verb subject) signals a question.

In either English or Spanish, you can use the verb subject ordering in a question ("I can have this cookie?") without too much change in meaning, because of the 'magic' of a question mark overriding the sentence structure meaning. If the phrase were spoken, you would have to end with an upward inspection.

In all of my experience dealing with the Spanish language, the word "can" (when used to ask for permission, in English) is never used, in Spanish, to ask for permission to do something.

PODER connotes "[the] power to do something'' (in Spanish), only.

Even the Spanish noun ''el poder'' means ""the power"".

So, 'CAN I look at the magazine' is simply not the way of asking someone permission to look at their magazine! (It only expresses "power", in Spanish.)

Puedo ver la revista?... Do I have the power to wrestle the magazine away from you so that I can look at it? (Get the point?)

We used to differentiate between may and can for this reason. People don't seem to do it much anymore. If you were to use may, it would be more directly petition the other person for permission.

Yes.

Yes, but only if you are asking if you have the power (ability) to look at the magazine. Even the Spanish noun el poder (not the verb) means ""the power"". So, if one is really interested in asking permission to look at their magazine, the person would not use poder, at all!

Me permites ver la revista?

(May I look at the magazine?)

'Can I see the magazine ?' is correct.