I'm probably making this much more difficult than it is, I'm also pretty sure that this is answered somewhere but I'm very tired of looking!

This has to do with an ice breaker and encountering a piece of ice. When encountering a piece of ice the first thing that matters is the strength of the two I think. If the strength of the ice breaker doesn't meet or exceed the ice then it is deflected. The sub routines then take effect as I understand it.

If the strength of the icebreaker does meet or exceed the the strength of the ice then the runner must have the correct type of icebreaker to defeat the subroutine or subroutines if there are multiple of the type of ice to avoid those but that doesn't cause the run to fail unless one of the subroutines is end the run. So if I understand a piece of ice that is a barrier can be passed by any icebreaker as long as the strength is high enough. The subroutines can not be bypassed unless the right type of breaker is being used! Am I correct?

You're correct, but be careful of terminology. 'Bypass' has a very specific meaning in Netrunner. A card that allows you to bypass means you skip over the ICE, ignoring effects without having to break it or suffer the effects.

If you suffer the effects of ICE but the run doesn't end, or if you broke the subroutines, you're considered to have 'passed' the ICE, not 'bypassed'. This can be important for some card effects.

So if I understand a piece of ice that is a barrier can be passed by any icebreaker as long as the strength is high enough. The subroutines can not be bypassed unless the right type of breaker is being used! Am I correct?

I have no idea what you mean by that first sentence. And subroutines are broken, not bypassed (bypassing is a different effect).

Example:

You have Battering Ram and Pipeline installed. You encounter a Neural Katana ( sentry ice, 3 strength, 1 subroutine: "Do 3 Net Damage"). You want to break Neural Katana's subroutine. Your Battering Ram only breaks barrier subroutines, so it's not going help, even though it's already 3 strength by default. You need to use Pipeline, as Pipeline breaks sentry subroutines. It only has a strength of 1, but it has an ability that let's you increase its strength by 1 by paying 2 credits. So you pay 4 credits to bring Pipeline up to strength 3. Now it can interact with Neura Katana to break its subroutine by using the "1 credit: break sentry subroutine" ability. After that, you can move on to the next ice (or the server, if Neural Katana was the last ice), or you can choose to jack out.

Alternatively, if you didn't have the credits or did not want to spend them but have the cards to spare, you can choose not to break the subroutine and suffer the subroutine's effect instead. No icebreaker is used in this case, so strength is completely irrelevant. After the subroutine has resolved, because there was no "end the run" subroutine, you can move on to the next ice (or the server, if Neural Katana was the last ice), or you can choose to jack out.

Ah, hang on, I'd missed that sentence Satsuoni. I think maybe I understand where that line comes from...

My apologies, I read the initial post on my phone while still in bed and I think sleep-fog was still in my brain. I see now that there is a misunderstanding in the OP.

Dartagnnon, when you make a run, you don't declare 'I'm making a run with Gordian Blade' (for example). You declare only the server you are making the run on.

When you encounter ICE, you may use any combination of programs to interact with that ICE, within the limitations of the programs themselves (i.e. Pipeline cannot break Barrier subroutines). However, if you have both Gordian Blade AND Pipeline, and encounter both Enigma and Neural Katana in the same run, you can break both, provided you have enough credits.

Alternatively, if you chose not to break the subroutines (or couldn't) you'd suffer the effects. Enigma, unbroken, will end the run, however Neural Katana will allow you to pass provided you survive the Net Damage.

The breakers you have installed are relevant ONLY if you're attempting to break. You can make a run with NO breakers installed if you wish. The runner, not the program, makes the run.

When all subroutines are either broken or resolved, the run continues (unless one of the unbroken subroutines stated 'End the Run'). You do not need to match strength AT ALL unless you are attempting to break subroutines.

Thanks for the clarification on what to do if a runner can not meet the strength of ICE (subroutines trigger, then end run since runner can't break the ice).

I found it odd that the rulebook doesn't seem to mention it too much (couldn't find a good clarification int he rulebook), and seems to be something important new players need to know.

Thanks for the clarification on what to do if a runner can not meet the strength of ICE (subroutines trigger, then end run since runner can't break the ice).

I found it odd that the rulebook doesn't seem to mention it too much (couldn't find a good clarification int he rulebook), and seems to be something important new players need to know.

The ICE only Ends the Run if the ICE has an Unbroken Subroutine that says "End the Run". If R&D is protected by one ICE and that ICE is Neural Katana and the Runner cannot or chooses not to break it, the Runner takes 3 Net Damage and may continue the Run.

Thanks for the clarification on what to do if a runner can not meet the strength of ICE (subroutines trigger, then end run since runner can't break the ice).

I found it odd that the rulebook doesn't seem to mention it too much (couldn't find a good clarification int he rulebook), and seems to be something important new players need to know.

I agree. I came here looking for clarification on this very thing, so thanks to all who helped out.

I thought the rule book explained it very well. It's not like I or anybody else who helps clarifying things has access to different sources. It's all in the rule book. It's just that people make assumptions about how stuff works and then don't read the instructions and examples properly. Case in point is kerred's comment, that summarizes a new player myth that we've explicitly tried to do away with in our explanations (the wrong assumption that ice ends the run if it is not broken, regardless of the nature of its subroutines).